Chapter 13.2, Problem 14PPS

To determine

To find: the probability that the Sylvie will be in the seat furthest from the entrance to the ride.

Answer to Problem 14PPS

The probability is $\frac{1}{8}$ .

Explanation of Solution

Given:

There are $8$ seats.

Concept used:

The number of ways of arranging $n$ item in order $=n!$ .

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

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

Calculation:

Since, the people are seated with a fixed reference point, this is a linear permutation. So, there are $8!$ or $40320$ ways in which the people can be seated. The number of favorable outcomes is the number of permutations of other $7$ people given that Sylvie will be in the seat farthest from the entrance to the ride, or $5040$ .

Therefore, the probability is:

  $\frac{5040}{40320}=\frac{1}{8}$ .

Hence, the probability is $\frac{1}{8}$ .