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 five different members. there are 17 qualified candidates, and officers can also serve on the committee. complete parts (a) through (c) below. a. how many different ways can the four officers be appointed? there are 57,120 different ways to appoint the four officers. b. how many different ways can a committee of five be appointed? there are 6,188 different ways to appoint a committee of five. c. what is the probability of randomly selecting the committee members and getting the five youngest of the qualified candidates? p(getting the five youngest of the qualified candidates)=□ (type an integer or a simplified fraction.)

Explanation:

Step1: Recall probability formula

The probability $P(E)$ of an event $E$ is given by $P(E)=\frac{n(E)}{n(S)}$, where $n(E)$ is the number of favorable outcomes and $n(S)$ is the number of total outcomes.

Step2: Identify number of favorable and total outcomes

The number of favorable outcomes $n(E)$ of getting the five - youngest candidates is 1 (since there is only one group of the five - youngest candidates). The number of total outcomes $n(S)$ of appointing a committee of five members out of 17 candidates is 6188 (from part b).

Step3: Calculate the probability

$P=\frac{n(E)}{n(S)}=\frac{1}{6188}$

Answer:

$\frac{1}{6188}$