a corporation must appoint a president, chief executive officer (ceo), chief operating officer (coo), and…

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.\na. how many different ways can the four officers be appointed?\nthere are different ways to appoint the four officers

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.\na. how many different ways can the four officers be appointed?\nthere are different ways to appoint the four officers

Answer

Explanation:

Step1: Identify the permutation formula

The number of permutations of $n$ objects taken $r$ at a time is $P(n,r)=\frac{n!}{(n - r)!}$. Here $n = 16$ (number of qualified candidates) and $r=4$ (number of officers to be appointed).

Step2: Calculate the factorial values

$n!=n\times(n - 1)\times\cdots\times1$. So $16! = 16\times15\times14\times13\times12\times\cdots\times1$ and $(16 - 4)!=12!=12\times11\times\cdots\times1$. Then $P(16,4)=\frac{16!}{(16 - 4)!}=\frac{16!}{12!}=16\times15\times14\times13$.

Step3: Perform the multiplication

$16\times15 = 240$, $240\times14=3360$, $3360\times13 = 43680$.

Answer:

43680