Five people want to rent the last two copies of a movie. How many ways can these five people rent the two movies?
A. 10
B. 9
C. 8
D. 7
E. 6

Question

Five people want to rent the last two copies of a movie. How many ways can these five people rent the two movies?
A. 10 
B. 9 
C. 8  
D. 7
E. 6

ybarrap · Answer

Take 5 people and group them into two groups, one of size 2 (the ones that get the copies) and the other of size 3 (the ones that don't get the copies):
$$
{{5}\choose{2}}=\cfrac{5!}{2!3!}
$$
This is because there are 5! ways to permute the 5 people, but 2! of them are the same combination, just in different order and similarly for the 3! of the second group.

Does this make sense?

anonymous · Answer

ohh i get it now
so the answer is 10?

ybarrap · Answer

yes!

anonymous · Answer

The answer is, "A". 10.

anonymous · Answer

whoops he already answered you. Sorry!