Problem

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 five different members. There are 11 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?
There are $\square$ different ways to appoint the officers.

Answer

Expert–verified
Hide Steps
Answer

Final Answer: \(\boxed{7920}\) different ways to appoint the officers.

Steps

Step 1 :The problem is asking for the number of ways to appoint 4 officers (president, CEO, COO, CFO) from 11 candidates. This is a permutation problem because the order of appointment matters (i.e., appointing person A as president and person B as CEO is different from appointing person B as president and person A as CEO). The formula for permutations is nPr = n! / (n - r)!, where n is the number of items to choose from, r is the number of items to choose, and ! denotes factorial.

Step 2 :Let's denote the number of candidates as n and the number of officers to be appointed as r. In this case, n = 11 and r = 4.

Step 3 :Substitute n = 11 and r = 4 into the permutation formula: nPr = n! / (n - r)!. This gives us the number of ways to appoint the officers.

Step 4 :Calculate the result to get the final answer.

Step 5 :Final Answer: \(\boxed{7920}\) different ways to appoint the officers.

link_gpt