Chapter 13.1, Problem 9CFU

To determine

To find: The value of $\frac{P\left(12,8\right)}{P\left(6,4\right)}$ .

Answer to Problem 9CFU

The value of $\frac{P\left(12,8\right)}{P\left(6,4\right)}$ is $554400$ .

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,

  $\begin{array}{c}\frac{P\left(12,8\right)}{P\left(6,4\right)}=\frac{\frac{12!}{\left(12-8\right)!}}{\frac{6!}{\left(6-4\right)!}}\\ =\frac{19958400}{360}\\ =554400\end{array}$