Chapter 12.4, Problem 22PPS

To determine

To find: the permutation that the person can arrange the necklaces in the display case.

Answer to Problem 22PPS

The person can arrange the necklaces in the display case in 1320 ways.

Explanation of Solution

Given information:

Total number of necklaces is 12.

The person has to place 3 necklaces in the display case out of 12.

Formula used:

  $P\left(n,r\right)=\frac{n!}{\left(n-r\right)!}$

Calculation :

Number of ways that the person can arrange the necklaces in the display case are-

  $\begin{array}{l}P\left(n,r\right)=\frac{n!}{\left(n-r\right)!}\\ P\left(12,3\right)=\frac{12!}{\left(12-3\right)!}\left[n=12\text{ and }r=3\right]\\ =\frac{12!}{9!}\\ =\frac{12\times 11\times 10\times 9!}{9!}\left[\text{Divide by common factor}\text{.}\right]\\ =1320\text{ ways}\end{array}$

Hence, there are 1320 ways that the person can arrange the necklaces in the display case.