There are ten movies that Greg would like to rent but the store only allows him to have four movies at one time In how many ways can Greg choose four of the ten?

Answer 1

The first movie he chooses can be any one of 10.

For each of these, the second one can be any one of the remaining 9.

For each of these, the third one can be any one of the remaining 8.

For each of these, the fourth one can be any one of the remaining 7. So there are (10 x 9 x 8 x 7) = 5,040 ways that he can pull four out of the pile of ten. If the order of the group of four doesn't matter, i.e. A-B-C-D is the same to Greg as C-B-D-A, then he can wind up with (5,040) / (4 x 3 x 2) = 5040/24 = 210 distinctly different groupsof four movies.