Question

A corporation must appoint a president, chief executive officer (CEO). chief operating (COO), and chief financial officer (CFO). It must also appoint a planning committee with three different members. There are 13 qualified candidates, and officers can also serve on the committee. Complete parts a through c below.

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 a specific group of the qualified candidates? P(getting a specific group of the qualified candidates) = ?

Answer 1

Answer: A corporation must appoint a president, chief executive officer (CEO). chief operating (COO), and chief financial officer (CFO). It must also appoint a planning committee with three different members. There are 13 qualified candidates, and officers can also serve on the committee.

Solution:

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

There are four officers selected from 13 qualified members.

n = 13

r = 4

Using the formula of permutation:

nPr = n!/(n-r)!

13P4 = 12!/(12-4)!

13P4 = 17160

Therefore, thereare 17160 different ways to appoint the officer.

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

There are 3 members selected from 13 qualified members.

n = 13

r = 3

13P3 = 286

Therefore, there are 286 different ways to appoint committee.

C. What is the probability of randomly selecting the committee members and getting a specific group of the qualified candidates?

P(getting a specific group of the qualified candidates) = 1/286 = 0.003497.

Therefore, probability of getting a specific group of the qualified members is 0.0035.