Question

Suppose that a company will select 3 people from a collection of 15 applicants to serve as a regional manager, a branch manager, and an assistant to the branch manager. In how many ways can the selection be made? Explain how you got your answer.

Answer 1

Answer: 2730

Explanation:

Given : The number of applicants =15

The number of posts for which candidates have been applied = 3

To find the number of selections we use permutations since here order matters.

The permutations of n things taking m at a time is given by :-

`^nP_m=(n!)/((n-m)!)`

Then , the required number of ways is given by [Put n = 15 and m = 3] :-

`^(15)P_3=(15!)/((15-3)!)\\\\=(15*14*13*12!)/(12!)\\\\15*14*13=2730`

Hence, the number of ways the selection can be made = 2730