Chapter 13.2, Problem 22E

To determine

To find: Whether the arrangement of object is linear or circular and the number of arrangements of each situation.

Answer to Problem 22E

The permutation is linear and the number of arrangements is $\frac{26!}{6!3!7!10}$ .

Explanation of Solution

Given information: A stack of $6$ pennies, $3$ nickels, $7$ dimes and $10$ quarter.

The problem represents a linear permutation with repetition so the number of arrangements is given by the formula $\frac{n!}{p!q!r!}$ .

The problem represents a linear permutation with repetition.

There are $26$ elements as $\left(6+3+7+10=26\right)$

The number of arrangements is given by using the given formula $\begin{array}{l}\left(\frac{n!}{p!q!r!}\right)=\frac{26!}{6!3!7!10}\\ \end{array}$ .

Therefore the number of arrangements is $\frac{26!}{6!3!7!10}$ .