There are 12 men at a dance.
(a) In how many ways can eight of them be selected to form a cleanup crew?
(b) How many ways are there to pair off eight women at the dance with eight of these 12 men?

Question

There are 12 men at a dance. 
(a) In how many ways can eight of them be selected to form a cleanup crew? 
(b) How many ways are there to pair off eight women at the dance with eight of these 12 men?

anonymous · Answer

In part (a), you want to take 12 C 8, which means a combination of 8 from 12, so use your calculator to see that 12 C 8 = 495.

Note, that I used a combination (not a permutation), because order does not count in this problem.

If I understand your part (b) correctly, there are 8! = 40,320 ways to pair these 8 men with a set of 8 women. (8! means 8 factorial).