Out of 12 books, you plan to take 5 with you. how many different collections of 5 books can you take?

Basically, you are asking how many ways can 5 objects be chosen from 12 (the order is NOT important).
The formula for this is n! / [ r! * (n-r)! ]
12! / [5! * 7!] =
12*11*10*9*8*7! / (5! * 7!) =
12*11*10*9*8 / 5 * 4 * 3 * 2 =
11*9*8 =
792 different collections

Source:
http://www.1728.org/combinat.htm