Chapter 13.2, Problem 6PPS

To determine

To find: the probability that Chad will seat $C11$ and Nia will be in $C12$ .

Answer to Problem 6PPS

The probability is $\frac{1}{132}$ .

Explanation of Solution

Given:

Nia and Chad are going to concert.

The seat of the club is shown in diagram as:

  

Concept used:

The probability formula is used to compute the probability of an event to occur as:

  $P\left(A\right)=\frac{\text{Number of favorable outcome}}{\text{Total Number of favorable outcomes}}$ .

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 seat is a way of arranging the students, order in this situation is important. There are $12$ seats. The number of possible outcomes in the sample space is the number of permutations of $12$ seats taken $2$ at a time.

  $P{}_2=\frac{12!}{\left(12-2\right)!}=\frac{12\times 11\times 10!}{10!}=132.$

Among these,there is only one particular arrangement in which chad will be in seat $C11$ and Nia will be in $C12$ therefore ,the probability is $\frac{1}{132}$ .

Hence, the probability is $\frac{1}{132}$ .