Chapter 13, Problem 18SGA

To determine

To find: The value of $\frac{P\left(6,3\right)}{P\left(5,3\right)}$ .

Answer to Problem 18SGA

The value of $\frac{P\left(6,3\right)}{P\left(5,3\right)}$ is $2$ .

Explanation of Solution

Consider the permutation of the n object taken $r$ at a time is,

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

Then,

  $\begin{array}{c}\frac{P\left(6,3\right)}{P\left(5,3\right)}=\frac{\frac{6!}{\left(6-3\right)!}}{\frac{5!}{\left(5-3\right)!}}\\ =\frac{\frac{6!}{3!}}{\frac{5!}{2!}}\\ =\frac{120}{60}\\ =2\end{array}$