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[TUSR]

If I need to find the new limits of integration for the function that I talked about above, do you just plug in the old limits of integration into the "u" term?

If so, how do I know whether to use degrees or radians?
The old limits of integration was [-2,3].

For u sub you don't NEED to switch your limits of integration. But sometimes it ends up making the problem easier.

Say you are integrating xsin(x^2)dx from 1 to 2.
Let u = x^2
Therefore du = 2xdx
dx = du/2x

You're left with the integral (1/2)sin(u) from u1 to u2.

At this point you can either switch your limits of integration and use those to find the definite integral. Or you can do the integral and then put x^2 back in to wherever there is u.

To switch limits of integration you can use your equation u=x^2 and plug your limits of integration into that and get new limits. For x = 1 to 2, u = 1 to 4.

Use radians. Always.

Wrote this on my phone, apologizes if something isn't clear. PM me if needed.

Switching limits method.

 

[AgentChris]

How would I simplify this radical expression?

√2x + 6√8x - 2√32x

= 5√2x

I need a step by step explanation because I messed up somewhere and got 4√2x

 

[Kazerei]

How would I simplify this radical expression?

√2x + 6√8x - 2√32x

= 5√2x

I need a step by step explanation because I messed up somewhere and got 4√2x

Maybe you're just missing the 1?

√2x + 6√4*2x - 2√16*2x

√2x + 6*2√2x - 2*4√2x

(1+12-8)√2x

5√2x

 

[AgentChris]

Maybe you're just missing the 1?

√2x + 6√4*2x - 2√16*2x

√2x + 6*2√2x - 2*4√2x

(1+12-8)√2x

5√2x

I did forget the 1, now I can move onto the next problem. Thank you Kazerei, you're awesome.

 

[Memento_Mori15]

B should be 60/100 = 3/5. For part C, let's change the denominators to 100 and then erase all the events that don't have a small ball since we're told a small ball is chosen.

(Red,small): 15/100 = .15
(Green, small): 20/100 = .2
(Yellow, small): 25/100 == .25

These 3 lines now consist of the entire sample space due to being given that we drew a small ball. The probabiliby that it was red is thus .15 / (.15 + .2 + .25) = .25

Must say, that's a better way to look at it.

Let's think about it a different way. How many different ways are there to choose the members of the first team? This would be (10; 5). Once you choose the first 5 members, the second team is decided. So the answer is (10; 5) = 252

So it is (10;5)? I was getting confused from the past posts saying it was something different. I wrote down (10;5) on my homework but I could be wrong..

A good way to do this one is to assume that the squares are ordered. This solves the order problem by only considering dominos where the first square is less than or equal to the second square.

Suppose the first square is 1, there are 9 choices for the second square. If the first square is 2, there are 8 choices for the second square (we're ignoring 2 / 1 because 1/2 was already counted by the previous step). etc. So we've got 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 9*10 / 2 = 45

Now I get the addition, but where did you get the 9*10/2?

http://www.artofproblemsolving.com/Store/viewitem.php?item=intro:counting

I admit that this series of books is geared towards competition mathematics, so it contains some very difficult problems, but at the same time this is the easier of the two probability books, and it does in fact go through all the basics. More importantly is that the explanations are excellent and very clear, and it teaches very intuitive and easy to understand strategies for solving counting problems. Plus, when you understand the explanations for the difficult problems, then the easy problems become trivial. FWIW, the problems don't just immediately start difficult, it just offers the more difficult ones for those who want to push their limits a bit further.

Thanks, I'll look into this book. Looking at the review from amazon also, it seems like a really useful book. So I just have to make sure I buy the solution manual with it. Thanks again for the help. Your username or tag should be the math_king. Been really helpful with all this discrete stuff.

Conditional probability formula works here.

We have A = {a small ball is chosen} and let's name B = {a red ball is chosen}.

P(B|A) = P( B and A both happens) / P(A happens)

P(B and A happens) is just the probability of having a small ball, with that ball being red. There's 15/100=0.15 chance of picking a small red ball.

P(A) = 60/100 = 0.6 as calculated before.

As such, P(B|A)= 0.15/0.6 = 15/60 = 1/4.

So I used the formula wrong..I should find my scrap paper and see where I messed up. Thanks man.

 

[kharma45]

I've tried this question, so has my brother and I even asked my parents. We all came to the same answer, it should be 375 people but there is no option for that. What am I missing here?

 

[thequickandthedead]

I don't remember how these things work at all, so don't listen to me making a fool of myself, I'm just having fun with wild guesswork and googling everything I don't remember.

But here's what I'd do:

You want P(X > 5) < 0.1 for a given period of time. Using a Poisson table with &#955; = 3.1, I got P(X>5) = 0.0942, which is just a little less than 0.1.

So, you want &#955; = 3.1. As we recall, &#955; is your mean rate. Your mean, here, is 0.6/h, or 0.6 / 60mins.

0.6/60mins is equivalent to 3.1/310mins. If you want &#955; = 3.1, your period of time must be 310 minutes.

Thanks. I checked your answer and you got it right.

 

[youngwerther]

I've tried this question, so has my brother and I even asked my parents. We all came to the same answer, it should be 375 people but there is no option for that. What am I missing here?

I think that the right answer is 405.

The amount of people you are looking for is 10% less than the 60% who said higher in year 2.

10% of 60 is 6.

60 minus 6 is 54.

x/750 = 54.

x= 405

 

[kharma45]

I think that the right answer is 405.

The amount of people you are looking for is 10% less than the 60% who said higher in year 2.

10% of 60 is 6.

60 minus 6 is 54.

x/750 = 54.

x= 405

Cheers! Seems to easy now, thanks for your help.

 

[LightOfTruth]

Can anyone here help with finding Region of Convergence? I never learned it in differential equations...

 

[cpp_is_king]

Cheers! Seems to easy now, thanks for your help.

Fwiw, this is a bad question. Your reasoning was perfectly sound, but the problem as written is ambiguous (ie does 10% less than 60% mean 50% or 54%?)

 

[cpp_is_king]

Now I get the addition, but where did you get the 9*10/2?

One of the most useful identities in discrete math sum of the first n integers is n(n+1)/2
Ex:
1+2+...+12345 = 12345(12346)/2 = 76,205,685

 

[cpp_is_king]

Ok my turn to ask for some help. I suck at this type of thing. I need a function f(x,y) = z that looks similar to the following graph:

Assume that the marked point with the highest z value is is given by (xm, ym, zm).

Note in particular that it is not a plane because dz/dy is not constant. Also note the two points marked at (0, ym, z1) and (xm, 0, z2). z1 != z2 here.


Ideally I would like the dz/dy to be exponential (which I tried to represent by the curved lines along the edges). Aside from that, I'm not too picky. If I get the basic structure of such a function, I can tweak the parameters myself for scaling, slope, etc.

Edit: I came up with z = log + x. Kind of obvious and a stupid question in hindsight.

 

[MisterLuffy]

I have a question:

After all students have left the classroom, a statistics professor notices that four copies of the text were left under desks. At the beginning of the next lecture, the professor distributes the four books in a completely random fashion to each of the four students (1, 2, 3, and 4) who claim to have left books. One possible outcome is that 1 receives 2's book, 2 receives 4's book, 3 receives his or her own book, and 4 receives 1's book. This outcome can be abbreviated as (2, 4, 3, 1).

a) List the other 23 possible outcomes.
b) Let X denote the number of students who receive their own book. Determine the pmf of X.

 

[DEATH™]

I have a question:

After all students have left the classroom, a statistics professor notices that four copies of the text were left under desks. At the beginning of the next lecture, the professor distributes the four books in a completely random fashion to each of the four students (1, 2, 3, and 4) who claim to have left books. One possible outcome is that 1 receives 2's book, 2 receives 4's book, 3 receives his or her own book, and 4 receives 1's book. This outcome can be abbreviated as (2, 4, 3, 1).

a) List the other 23 possible outcomes.
b) Let X denote the number of students who receive their own book. Determine the pmf of X.

Based on the questions, it wants you to do them manually... It's pretty straigthforward honestly...

a)As it said, write all the possible outcomes. This is pretty much a permutation of some sorts. So you would prefer to make a systematized way to get all the possibilities.

example: (1,2,3,4),(1,2,4,3),(1,3,2,4),(1,4,2,3)...

b)Now the whole set of possibilities gets in handy. There are total of 24 possible outcomes, so each choice has a probability of 1/24 chance of happening. Now it's asking "how probable that you can hand X number of students their right book?". So the possible values of X is from 0 (nobody gets the right books) to 4 (all 4 students get the right book). So you just need to look up the possibilities and count them up depending on the X you are looking for...

Hope this helps.

 

[MisterLuffy]

Based on the questions, it wants you to do them manually... It's pretty straigthforward honestly...

a)As it said, write all the possible outcomes. This is pretty much a permutation of some sorts. So you would prefer to make a systematized way to get all the possibilities.

example: (1,2,3,4),(1,2,4,3),(1,3,2,4),(1,4,2,3)...

b)Now the whole set of possibilities gets in handy. There are total of 24 possible outcomes, so each choice has a probability of 1/24 chance of happening. Now it's asking "how probable that you can hand X number of students their right book?". So the possible values of X is from 0 (nobody gets the right books) to 4 (all 4 students get the right book). So you just need to look up the possibilities and count them up depending on the X you are looking for...

Hope this helps.

Thanks....

 

[cpp_is_king]

Thanks....

You can also do it with counting arguments instead of going through every permutation. let's say we're looking at X=0. That is, none of the people got their own book. Start with person 1. There are 3 possible books he could have received. Let's say he received book 2 (although the argument is the same regardless).

2 _ _ _ {remaining: 1 3 4}

In slot 2, any of the 3 remaining books can be placed there. Regardless of which book you place there, there is only 1 choice remaining. Thus,

pmf(X=0) = 3 x 3 = 9


Now let's consider X=1. First we choose the person who got his own book. There are 4 ways to do this. Then similar to the case with X=0, we write it down

1 _ _ _ {remaining: 2 3 4}

Nobody else can receive their own book here. So there are 2 possible books person 2 can receive, and regardless of which one he receives, person 3 and 4 are decided. Thus,

pmf(X=1) = 4x2 = 8

Now let's consider X=2. This time we choose the two people who got their own book. There are (4; 2) = 4!/(2!2!) = 6 ways to do this. Again, we write down the example:

_ 2 _ 4 {remaining: 1 3}

There is only 1 way to distribute the remaining 2 books, so we have:

pmf(X=2) = 6x1 = 6

For X=3, notice that there are 0 ways this can happen. If you give 3 people the correct book, there is only 1 book left, it has to go to the correct person!

So pmf(X=3) = 0

For X=4, there is clearly only 1 way.



Summarizing:

PMF(X=0) = 9/24
PMF(X=1) = 8/24
PMF(X=2) = 6/24
PMF(X=3) = 0/24
PMF(X=4) = 1/24

I'm not sure if there's a way to summarize this elegantly as a function of X. In any case, you can confirm that 9+8+6+0+1 = 24, so we've counted every single outcome.

 

[Orbis Tabula]

I had a multivariable calculus problem that involves taking the derivative using the Chain Rule. When I solve it using substitution, I'm getting a different error. I was just wondering if someone could walk me through using the chain rule on a problem like this so I can see what I'm doing wrong.

V(x,y,z)=(x-y)/(y+z)
x(t)=t, y(t)=2t, z(t)=3t

If I just plug in the x, y, and z values and derive w.r.t t, I get 0. But I'm not getting anything like that when I try to apply the chain rule.

EDIT: Oops. Strike that. As soon as I typed this I went back to thinker and I caught the small error that threw everything off. I've got it now.

 

[Kimosabae]

Could anyone recommend any good sources for developing word problem skills? Converting word problems to linear equations (for systems of equations), specifically.

 

[jerry1594]

Gaf I'm really bad at math. Right now I'm talking precalc, and given that I've missed like 2/7 classes (including the first one), and that the last comparable math class I took was algebra 2 like 2 years ago, I'm so lost. I have a midterm on the 30th. Any advice?

 

[Partial Gamification]

Gaf I'm really bad at math. Right now I'm talking precalc, and given that I've missed like 2/7 classes (including the first one), and that the last comparable math class I took was algebra 2 like 2 years ago, I'm so lost. I have a midterm on the 30th. Any advice?

Routine daily practice. It sucks, you can easliy fall off track, but it is the true way. Post your questions here.

What is pre-Calc anyway? Like trig and a college level algebra? Talking about what a function is and that sort of thing? Graphing equations?

edit: I'm not trying to be condescending, its like learning a foreign language that few people (not me) are immersed in and completely fluent with.

 

[TUSR]

Gaf I'm really bad at math. Right now I'm talking precalc, and given that I've missed like 2/7 classes (including the first one), and that the last comparable math class I took was algebra 2 like 2 years ago, I'm so lost. I have a midterm on the 30th. Any advice?

figure out what you need to learn, get the notes and study it????????????????????

 

[Kimosabae]

Routine daily practice. It sucks, you can easliy fall off track, but it is the true way. Post your questions here.

What is pre-Calc anyway? Like trig and a college level algebra? Talking about what a function is and that sort of thing? Graphing equations?

Yup. Where are you from? Pre Calc has become pretty pervasive in America the last 10 years or so.

 

[Partial Gamification]

Yup. Where are you from? Pre Calc has become pretty pervasive in America the last 10 years or so.

A different, older, set of standards. I could have googled a syllabus.

 

[Memento_Mori15]

Gaf I'm really bad at math. Right now I'm talking precalc, and given that I've missed like 2/7 classes (including the first one), and that the last comparable math class I took was algebra 2 like 2 years ago, I'm so lost. I have a midterm on the 30th. Any advice?

Unless you're good at math or find it easy, you can't really cram it(I highly don't recommend doing this!!). I could only do this till calculus. Being in calc 2, I knew I couldn't just cram it so I looked up videos, did hw problems, did recommended test problems, odd problems(they usually have the answers in the back to check), etc.

So you have 10 days to prepare, go over what you learned. Don't get a concept? You can post here or youtube the concept behind it. I suggest patrickjmt; goes straight into the core. Want a more detail explanation? You go to khan. Go through what you did and be sure you understand it. Do more problems outside the ones you were assigned. If you don't get the problem, again, post here. There's really not much to it.

 

[jerry1594]

Guess I'm going to have to buckle down and give it my best shot. Organization has been a huge problem with me always. Given that my classes are over 3 hours long, cramming doesn't seem so daunting and I figure setting aside a few hours a day this week I'll be on track soon.

 

[Aeris130]

Any graph-experts here? I've spent days pondering how to find the infinite/unbounded/external face of a graph component, given a planar circular embedding of adjacent edges around every vertex and a set containing all face cycles of the graph (generated from the embedding).

I realize the unbounded face will be traversed in the opposite clockwise direction as every other face, and it's easy to confirm that this is the case by visualizing the faces that the embedding gives. But I can't come up with an algorithmic solution that yields true/false based only on the embedding and a potentially unbounded face cycle.

 

[TUSR]

Guess I'm going to have to buckle down and give it my best shot. Organization has been a huge problem with me always. Given that my classes are over 3 hours long, cramming doesn't seem so daunting and I figure setting aside a few hours a day this week I'll be on track soon.

every hour in a calculus class is atleast another 1-2 hours of studying.

 

[jerry1594]

every hour in a calculus class is atleast another 1-2 hours of studying.

I've got nothing but time. I got to school five days a week. Mondays and Wednesdays I have math class from 9:50-1:10. Tuesdays and Thursdays I have French from 5:10-6:50, and Saturday morning I have a dumb class my advisor told me to sign up for from 9-12. Other than that all hours are free. What bites me in the ass and has always done so is my total lack of organization. Can't go on like this. I'm totally out of the loop in math and I bombed my French midterm.

 

[Memento_Mori15]

Guess I'm going to have to buckle down and give it my best shot. Organization has been a huge problem with me always. Given that my classes are over 3 hours long, cramming doesn't seem so daunting and I figure setting aside a few hours a day this week I'll be on track soon.

When I said cramming, it was the day before cramming lol. That is what I don't recommend.

 

[youngwerther]

Gaf I'm really bad at math. Right now I'm talking precalc, and given that I've missed like 2/7 classes (including the first one), and that the last comparable math class I took was algebra 2 like 2 years ago, I'm so lost. I have a midterm on the 30th. Any advice?

Take a hard look at the syllabus and identify the key concepts.

Get the book and look over those chapters.

Follow along with the examples that are worked in the chapter.

Watch youtube videos/khan academy of what you are learning.

Go back to book chapter and work exercises.

Routine daily practice. It sucks, you can easliy fall off track, but it is the true way. Post your questions here.

What is pre-Calc anyway? Like trig and a college level algebra? Talking about what a function is and that sort of thing? Graphing equations?

edit: I'm not trying to be condescending, its like learning a foreign language that few people (not me) are immersed in and completely fluent with.

Kind of.

When I took it, it was stuff like

Radian measure
Unit Circle
College-level trig
Vectors
Polar Coordinates
Summation Notation
Harmonic motion
Conic Sections

Shit like that.
I'm probably forgetting a lot.


I'm so glad I took it before going to calculus, it was a BIG help.
I was sitting in my Calculus 2 class today, we were going over L'Hopital's Rule and there were people who were getting confused at compound fractions and didn't know how to evaluate limits.
I was just like "god damn, how do you people have a better grade in here than me. oh wait because I never come to class. but at least i know what the fuck a compound fraction is, jesus"

Some girl said the following, and I repeat verbatim - "Wait, you can divide by something that is being divided by something?"

 

[Exuro]

So I'm taking discrete and I'm wondering if anyone knows what (a',b') means compared to just an arbitrary (a,b).

Trying to prove if a relation T is a partial order and I need to understand what that coordinate means.

 

[TUSR]

a' b' are usually when you transform your function into another



quick example.

 

[Exuro]

a' b' are usually when you transform your function into another

http://i.imgur.com/kJfn525.png[IMG]

quick example.[/QUOTE]Hmm I'm pretty sure it isn't that. The problem involved proving is a relation is a partial order or not, and part of the relation gives the arbitrary elements ((a,b),(a',b')).

 

[TUSR]

Hmm I'm pretty sure it isn't that. The problem involved proving is a relation is a partial order or not, and part of the relation gives the arbitrary elements ((a,b),(a',b')).

yeah i was trying to relate discrete to calc haha, sorry man

 

[Partial Gamification]

So I'm taking discrete and I'm wondering if anyone knows what (a',b') means compared to just an arbitrary (a,b).

Trying to prove if a relation T is a partial order and I need to understand what that coordinate means.

I'm not certain but check this out.

Looks like (a,b) is the in the domain and (a',b') is in the codomain, f is the order preserving function; f: (a,b) -> (a',b').

 

[Globox_82]

can someone help me with this?
Y=70*0,855^x
can also be written as Y=70*e^kx

The question is. Find k with 3 decimal numbers.
Have no idea how.

Correct response on is k= -0.157
But do I get there?

 

[Kazerei]

can someone help me with this?
Y=70*0,855^x
can also be written as Y=70*e^kx

The question is. Find k with 3 decimal numbers.
Have no idea how.

Correct response on is k= -0.157
But do I get there?

0,855^x = (e^-0.157)^x = e^(-0.157x)

 

[Leezard]

can someone help me with this?
Y=70*0,855^x
can also be written as Y=70*e^kx

The question is. Find k with 3 decimal numbers.
Have no idea how.

Correct response on is k= -0.157
But do I get there?

Google natural logarithm.

 

[Globox_82]

0,855^x = (e^-0.157)^x = e^(-0.157x)

ok how about this:

Value y on a car diminishes based on this function

Y=225000 * e^-kx

X is cars age in years and K is a constant.

When X=5 value on car is 100000.
Find constant K

Thanks

 

[The One Who Knocks]

ok how about this:

Value y on a car diminishes based on this function

Y=225000 * e^-kx

X is cars age in years and K is a constant.

When X=5 value on car is 100000.
Find constant K

Thanks

I hope you don't mind that I did it on paper and took a picture since I find it far easier than typing it out (my writing is bad so apologies if it's unclear), I've gone through it step by step:

I assume the problem you are having is at the "ln(4/9)" line and I've tried to write an explanation (avoiding the use of variables so you can get a 'practical' example) here as to what happens if this is the case:

As I've pretty much done the question, here is a very similar one if you want to practice a similar style question:

EDIT: Actually, in case you are looking for the solutions after you've done it (if you want of course) they're here:

Spoiler

http://www.studentxpress.ie/ProjectMaths/HLSPASoln(P1Q4).pdf

.

 

[Kazerei]

ok how about this:

Value y on a car diminishes based on this function

Y=225000 * e^-kx

X is cars age in years and K is a constant.

When X=5 value on car is 100000.
Find constant K

Thanks

Sounds like you're just starting to learn about logarithms. If you don't have good notes or textbook, try Khan Academy

https://www.khanacademy.org/math/algebra/logarithms-tutorial

 

[cpp_is_king]

can someone help me with this?
Y=70*0,855^x
can also be written as Y=70*e^kx

The question is. Find k with 3 decimal numbers.
Have no idea how.

Correct response on is k= -0.157
But do I get there?

The inverse of addition is subtraction. To find the value of Y in Y + 4 = 3, you subtract 4 from both sides.

The inverse of raising to a power is a logarithm. To find the value of Y in 3 = 2^Y, you take the logarithm of both sides.


To apply this to this problem, you've got two equations which are both Y. Set them equal.

70*0.855^x = 70*e^kx

0.855^x = e^kx

Now as just discussed, take the logarithm of both sides:

ln(0.855^x) = ln(e^kx)

x ln(0.855) = kx ln(e)

x ln(0.855) = kx

ln(0.855) = k

 

[Globox_82]

Sounds like you're just starting to learn about logarithms. If you don't have good notes or textbook, try Khan Academy

https://www.khanacademy.org/math/algebra/logarithms-tutorial

I hope you don't mind that I did it on paper and took a picture since I find it far easier than typing it out (my writing is bad so apologies if it's unclear), I've gone through it step by step:



I assume the problem you are having is at the "ln(4/9)" line and I've tried to write an explanation (avoiding the use of variables so you can get a 'practical' example) here as to what happens if this is the case:



As I've pretty much done the question, here is a very similar one if you want to practice a similar style question:


EDIT: Actually, in case you are looking for the solutions after you've done it (if you want of course) they're here:

Spoiler

http://www.studentxpress.ie/ProjectMaths/HLSPASoln(P1Q4).pdf

.

The inverse of addition is subtraction. To find the value of Y in Y + 4 = 3, you subtract 4 from both sides.

The inverse of raising to a power is a logarithm. To find the value of Y in 3 = 2^Y, you take the logarithm of both sides.


To apply this to this problem, you've got two equations which are both Y. Set them equal.

70*0.855^x = 70*e^kx

0.855^x = e^kx

Now as just discussed, take the logarithm of both sides:

ln(0.855^x) = ln(e^kx)

x ln(0.855) = kx ln(e)

x ln(0.855) = kx

ln(0.855) = k

Thank you all ( even those that I didn't quote).

One more follow up question


x ln(0.855) = kx ln(e) - what happens with ln(e) ? Why it disappears? You can't run ln(e) in calculator, and ln on the other side stays...so what happens with it?

x ln(0.855) = kx

ln(0.855) = k

 

[Leezard]

ln(e) = 1

 

[Globox_82]

ln(e) = 1

...now I remember. thanks

 

[Memento_Mori15]

Remember that basketball problem I posted back:

the answer was choose (10 5)/2. Explanation: We counted each division into the two teams twice. Once when the first 5 were chosen and again when the 5 others were. Now I get it after the explanation but when exam time come, I don't want to mess up. Is there a way to know when to divide your initial outcome? Is there an alternate way to think of this problem and arriving to the same answer?

Also, what does this mean:

I've seen it before but I really can't recall it at the moment. What does it mean?

 

[Partial Gamification]

Remember that basketball problem I posted back:

the answer was choose (10 5)/2. Explanation: We counted each division into the two teams twice. Once when the first 5 were chosen and again when the 5 others were. Now I get it after the explanation but when exam time come, I don't want to mess up. Is there a way to know when to divide your initial outcome? Is there an alternate way to think of this problem and arriving to the same answer?

Also, what does this mean:

I've seen it before but I really can't recall it at the moment. What does it mean?

Twelve Grams? The ninth dozen? It looks like an indexing, or some bad combinatorial notation.

Its messed up because of the confusion between nPr (nPk above) and nCr; permutations and combinations.

It could mean other things too, this just seems the most fitting.

 

[youngwerther]

I'm trying to evaluate this indefinite integral and am not sure what to make u

(sinhsqrt(x))/sqrt(x) dx

edit: Nevermind, figured this one out.
Will probably be back in a bit.

 

[cpp_is_king]

Remember that basketball problem I posted back:

the answer was choose (10 5)/2. Explanation: We counted each division into the two teams twice. Once when the first 5 were chosen and again when the 5 others were. Now I get it after the explanation but when exam time come, I don't want to mess up. Is there a way to know when to divide your initial outcome? Is there an alternate way to think of this problem and arriving to the same answer?

I kind of disagree with the answer, but only becomes it comes down to ambiguity, and both answers are correct depending on how you interpret the problem. The answer you gave and that we discussed, which was (10; 5) assumes that the two teams are considered different. The answer expected treats both teams as identical.

What i mean by this is, you could resolve the ambiguity with the following problem statement. "You've got the Lakers and the Bulls, and 10 players. 5 players need to go to the Lakers and 5 players need to go to the Bulls. How many ways are there to do this?" In this case it's clear that the two teams are different, and that if Hakeem Olajuwon is on the Lakers, it's different than if Hakeem Olajuwon is on the Bulls. The answer to this problem is unambiguously (10; 5).

Apparently the way they wanted you to interpret the problem is to assume that you're just forming two random teams with no team-based identity.

One way to help when it comes to exam time is perhaps to reduce it to a simpler problem. For example, suppose there are only 2 people, and we are trying to figure out how to divide them into 2 teams of 1 player each. Our method would have shown that the answer is 2, and the "correct" method would have shown that the answer is 1. Now it's obvious why there's a difference. Our method treats the configurations A | B and B | A as different, and the correct method does not.

When in doubt, ask the instructor whether the groups are distinguishable. Sometime teachers are hesitant to answer questions because they feel like you're fishing for hints. So if you specifically use the word "distinguishable", it should emphasize that you're only asking for clarity about the problem statement, and that you are specifically trying to choose between 2 different answers but that the problem statement is ambiguous.