Question

Deshawn has five CDs that he is going to give away. He lets his best friend choose three of five CDs. How many different groups of three CDs are possible?

Answer 1

10 different groups of three CDs are possible

Explanation:

Total CDs are five and 3 has to be chosen where order doesn't matter.

In these kind of scenarios, combinations are used for calculating different ways in which the CDs can be given.

So,

Number of ways in which groups of CDs are possible = ⁵C₃

`= (n!)/(r!(n-r)!) \\= (5!)/(3!(5-3)!)\\=(5!)/(3!2!)\\=(5*4*3!)/(3!2!)\\=(5*4)/(2)\\=(20)/(2)\\=10`

Therefore, 10 different groups of three CDs are possible ..