The wizard has 25 skills, each with 5 rune combinations (assuming we don't allow unruned skills), and 15 passives. With 6 skill slots and 3 passive slots, that gives us:
1,259,070,313,000 (1 trillion, 259 billion, and change)
Similarly, the other classes have:
Barb: 22 primary / 16 passive =652,863,750,000 (652 billion and change) barbarian builds
DH: 23 primary / 15 passive = 717,670,078,100 (717 billion and change) demon hunter builds
Monk : 21 primary / 14 passive = 308,626,500,000 (308 billion and change) monk builds
WD: 22 primary / 15 passive = 520,451,796,900 (520 billion and change) witch doctor builds