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)= (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)= (5!)/(3!2!)= (5*4*3*2*1)/(3*2*1*2*1)= (5*4)/(2)=10`

Answer: 10