Data management question?

Question

Five different cd-rom games: a,b,c,d,e are offered as a promotion by sugar rush cereal. one game is randomly included with each box of cereal.
determine the probability of getting all 5 games if 12 boxes are purchased?

Answer 1

Corrected at end...

You will get 12 games.

Out of these 12 you want 5 to be different:

Ways to put 5 games in the 12 boxes, without replacement, no regard to order:

12C5 = 792

Divided by the total number of ways to put 5 games into the boxes:

5^12 = 2.44E8

792/2.44 = 3.22E-6 (seems way too small)

Correction:

The denominator is the total number of sequences. The numerator should be the number of sequences satisfying the event. I need to multiply 792 by 5^7 because we don't care about the other 7 boxes

P = 792*5^7/5^12 = 792/5^5 = 0.2534 , much more reasonable.