Chapter 13.2, Problem 2CYU

To determine

To find: the probability that chase is selected for lighting, Jaden selected for props and Emelina for spotlighting.

Answer to Problem 2CYU

The Probability is $\frac{1}{4896}$ .

Explanation of Solution

Given:

English class of $18$ students.

  $3$ members of the crew are selected random.

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:

Since choosing students for the particular roles is a way of ranking the members, order in this situation is important. The number of possible outcomes in the sample space is the number of permutations of  $18$ people taken  $3$  at a time,  $P{}_3$ .

  $P{}_3=\frac{18!}{\left(18-3\right)!}=\frac{18\times 17\times 16\times 15!}{15!}=4896.$

Among these, there is only one particular arrangement in which Chase is selected for lighting, Jaden is selected for props, and Emelina for spotlighting. Therefore, the probability is $\frac{1}{4896}$ .

Hence, the probability is $\frac{1}{4896}$ .