Chapter 13.2, Problem 34E

(a)

To determine

To find: The number of ways to name the point on the circle.

Answer to Problem 34E

The number of possible ways are $720$ .

Explanation of Solution

Given:

The given figure is as follows.

  

Calculation:

The problem is a circular permutation of $7$ elements.

The number of possible ways will be as follows.

  $\begin{array}{c}\left(n-1\right)!=\left(7-1\right)!\\ =6!\\ =720\end{array}$

Therefore, the number of possible ways are $720$ .

(b)

To determine

To find: The number of possible arrangements.

Answer to Problem 34E

The number of possible arrangements are $5040$ .

Explanation of Solution

Given:

The given figure is as follows.

  

Calculation:

In this case, the permutation becomes linear.

The number of possible arrangements will be as follows.

  $\begin{array}{c}n!=7!\\ =5040\end{array}$

Therefore, the number of possible arrangements are $5040$ .