Chapter 13.2, Problem 23HP

To determine

To Find: Whether the probability is that the particular object will be in the $nth$ position sometimes, always, or never $\frac{1}{n}$ is true or not.

Answer to Problem 23HP

The given statement is false.

Explanation of Solution

Given:

The number of boys is 15 and the number of girls is 15.

The number of movie tickets is 4.

Calculation:

Consider the number of permutations with the n objects is $\left(n-1\right)!$ .

The case when the particular object is placed at the particular place then the remaining $\left(n-1\right)$ are to be arranged in the circular permutations in circular in $\left(n-2\right)!$ ways.

Then, the probability is that the particular object will be in the $nth$ position sometimes, always, or never $\frac{1}{n}$ is,

  $\begin{array}{c}\frac{\left(n-2\right)!}{\left(n-1\right)!}=\frac{1}{n-1}\\ \ne \frac{1}{n}\end{array}$

Thus, the given statement is false.