Question

A corporation must appoint a​ president, chief executive officer​ (CEO), chief operating officer​ (COO), and chief financial officer​ (CFO). It must also select​ a planning committee with five different members. There are 17 qualified​ candidates, and officers can also serve on the committee. How many different ways can the committee be​ appointed?

Answer 1

There are 524,560 ways that the committee can be​ appointed.

Explanation:

There are 9 different positions, a president, 3 officers and five committee members.

So

P - O1 - O2 - O3 - C1 - C2 - C3 - C4 - C5

There are 17 candidates, any of them can be president. So P = 17.

All of the others can be an officers. So O1 = 16, O2 = 15(17 subtracted by the president and O1), O3 = 14.

The officers can be committee members, so, C1 = 16, C2 = 15, C3 = 14, C4 = 13, C5 = 12.

How many different ways can the committee be​ appointed?

This is the sequence C1...C5:

`N = 16*15*14*13*12 = 524,560`

There are 524,560 ways that the committee can be​ appointed.