Question

A corporation must appoint a​ president, chief executive officer​ (CEO), chief operating officer​ (COO), and chief financial officer​ (CFO). It must also appoint a planning committee with four different members. There are 13 qualified​ candidates, and officers can also serve on the committee. A. How many different ways can the officers be​ appointed?B. How many different ways can the committee be​ appointed?

C. What is the probability of randomly selecting the committee members and getting the four youngest of the qualified​candidates?

Answer 1

A) 715 ways

B) 715 ways

C) (1/715)

Explanation:

This is a permutation and combination problem.

Since we want to select a number of people from a larger number of people, we use combination as the order of selection isn't important now.

A) How many different ways can the officers be appointed?

There are 4 officer positions.

There are 13 people in total.

We want to select 4 people from 13

Number of ways to select 4 people from 13 = ¹³C₄ = 715

B) How many different ways can the committee be appointed?

Number of committee members = 4

Total number of people available = 13

Number of ways to select 4 people from 13 = ¹³C₄ = 715

C) What is the probability of randomly selecting the committee members and getting the four youngest of the qualified candidates?

Selecting a group of the youngest candidates is just 1 amongst the total number of ways the 4 committee members can be picked,

Hence, the required probability = (1/715)

Hope this Helps!!!