Question

Solve the following problems using permutations or combinations. For each problem clearly identify which type it is and what your final answer is. You may use the calculator commands or the formula. a) A group of 30 people are to elect specific officers. They need to select a president, vice-president, secretary, treasurer, and historian. b) How many different ways can a telemarketer select 5 phone numbers from a list of 50?

Answer 1

Given data:

The total numbers of people are n=30.

(a)

The expression for the number of ways to select president, vice-president, secretary, treasurer, and historian is,

$\begin{gathered} x=^{30}P_5 \\ =\frac{30!}{(30-5)!} \\ =\frac{30!}{25!} \\ =17,100,720 \end{gathered}$

Thus, there are 17,100,720 ways to select president, vice-president, secretary, treasurer, and historian.