Question

Manuel has 6 CDs that he is going to give away. He lets his best friend choose 3 of the 6 CDs. How many different groups of 3 CDs are possible?

Answer 1

20 groups

Explanation:

The number of different groups possible to choose from would be the combination because order doesn't matter.

Ways of choosing r things from n total things in combination is given by:

`nCr = (n!)/((n-r)!*r!)`

Where

n ! = n * (n-1) * (n-2) * ....

So here we use

n = 6

r = 3

substituting in formula we get:

`nCr = (n!)/((n-r)!*r!)\\6C3 = (6!)/((6-3)!*3!)\\6C3=(6*5*4*3!)/(3!*3*2*1)\\6C3=5*4=20`

So, 20 groups are possible