Question

Eric has 5 CDs that he is going to give away. He lets his best friend choose 3 of the 5 CDs. How many different groups of 3 CDs are possible?

Answer 1

Given a group of n object. We want to make a selection of k objects out of the n object. This can be done in 

C(n, k) many ways, where $C(n, k)= \frac{n!}{k!(n-k)!}$,

where k!=1*2*3*...(k-1)*k


Thus, we can do the selection of 3 cd's out of 5, in C(5,3) many ways, 

where 

$C(5, 3)= \frac{5!}{3!2!}= \frac{5*4*3*2*1}{3*2*1*2*1}= \frac{5*4}{2}=10$

Answer: 10