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 three different members. there are 16 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 43680 different ways to appoint the four officers.
b. how many different ways can a committee of three be appointed?
there are 560 different ways to appoint a committee of three.
c. what is the probability of randomly selecting the committee members and getting the three youngest of the qualified candidates?
p(getting the three 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 total number of possible outcomes.

Step2: Identify $n(E)$

The number of ways to get the three - youngest candidates (favorable outcome) is $n(E) = 1$ since there is only one group of the three - youngest candidates.

Step3: Identify $n(S)$

From part (b), the total number of ways to appoint a committee of three is $n(S)=560$.

Step4: Calculate the probability

$P=\frac{n(E)}{n(S)}=\frac{1}{560}$

Answer:

$\frac{1}{560}$