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

(a)no. of ways=12c8=12c(12-8)=12c4=12*11*10*9/(4*3*2*1)=11*5*9=495
(b)no. of ways 8 men can be selected to form pairs with women=12c8=495
8 women can be selected in ways=8!
total no of ways=495*8!