A corporation must appoint a president, chief executive officer (CEO), chief ope

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 12 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 the four youngest of the qualified candidates?

Explanation / Answer

There are 4 different members, out of which 3 are officers post and 1 is president .

There are 12 candidates in total

a) This is a selection problem. so we need to select 3 officers out of 12

using the combination formula nPr = n!/(n-r)! , we get

12!/9! =

= 1320

b)

number of ways of appointing the positions and changing the president positions is

12C4 =

C(n,r)=C(12,4)C(n,r)=C(12,4)

=12!(4!(124)!)=12!(4!(124)!)

= 495

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