Chapter 13.2, Problem 13PPS

To determine

To find: the probability that Keith will be in the desk closest to the door.

Answer to Problem 13PPS

The probability is $\frac{1}{7}$ .

Explanation of Solution

Given:

There is a $7$ desk in the circle.

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 $7!$ or $5040$ ways in which the people can be seated. The number of favorable outcomes is the number of permutations of the other $6$ people given that Keith will be in the desk closest to the door.

  $6!$ or $720$ .

Therefore, the probability is $\frac{720}{5040}=\frac{1}{7}$ .

Hence, probability is $\frac{1}{7}$ .