Question

A club with five members will randomly select the president and vice president. Each possible pair will be assigned an equal portion of the interval from 0 to 1. Then a random number generator producing numbers in this interval will determine the outcome. Into how many parts should the interval be divided?

A. 9
B. 10
C. 20
D. 25

Answer 1

C. 20

Explanation:

There are 5 possible candidates for president.

After the president is selected, there are 4 remaining possible candidates for vice president.

Therefore, the number of permutations is 4 × 5 = 20.

Answer 2

C. 20

Explanation:

The order in which the members are selected is important. The first one selected is the president and the second is the vice president.

So we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

`P_((n,x)) = (n!)/((n-x)!)`

In this problem:

2 people are going to be chosen from a set of 5. So

`P_((5,2)) = (5!)/((5-2)!) = 20`

So the correct answer is:

C. 20