Chapter 13.2, Problem 29STP

To determine

To find: the probability that girl will be at each end of the row and choose the correct option.

Answer to Problem 29STP

The correct option is $C$ which is $\frac{1}{6}$ .

Explanation of Solution

Given:

Four members of pep band, two girls and two boys.

Concept used:

According to the permutation formula:

  $P{}_r=\frac{n!}{\left(n-r\right)!}.$

Where $P$ is the permutations.

  $n$ is the total number of objects in the set.

  $r$ is the total number of objects in the set.

Calculation:

There are $P{}_4=\frac{4!}{0!}=24$ ways to arranger the band. Out of these, there are $2!$ or $2$ ways to arrange the $2$ boys in the middle of the two girls at the end and for each arrangement there is an alternate arrangement by interchanging the position of the two girls.

Therefore, the probability is $\frac{4}{24}=\frac{1}{6}$ .

Hence, the correct option is $C$ which is $\frac{1}{6}$ .