Question

A club with 16 members is to choose three officers president vice president and secretary treasurer if each office is to be held by one person and no person can hold more than one office in how many ways can those offices be filled?

Answer 1

Answer:

The offices can be filled in 3,360 ways

Step-by-step explanation:

In this question, we are faced with a selection problem.

There are three offices and 3 officers to be selected.

For the first position, we are to select 1 out of 16. Now, for the second position, we are left with 15 members from which we are to select one. This is because the first selection has been picked and cannot partake in the subsequent selections.

Likewise for the third position, we are selecting 1 out of 14

The number of ways this can be done is thus; 16C1 × 15C1 × 14C1 = 16 × 15 × 14 = 3,360 ways