Chapter 8, Problem 66CR

To determine

To evaluate: The value of ${}_6{P}_4$ .

Answer to Problem 66CR

The value of ${}_6{P}_4$ is $360$ .

Explanation of Solution

Given:

The permutation ${}_6{P}_4$ .

Formula used:

The number of the permutations of $n$ elements taken $r$ at a time is calculated using the formula

  $\begin{array}{c}{}_n{P}_r=\frac{n!}{\left(n-r\right)!}\\ =n\left(n-1\right)\left(n-2\right)\mathrm{...}\left(n-r+1\right)\end{array}$

Calculation:

In ${}_6{P}_4$ the value of $n=6$ and $r=4$ .

Substitute these values in ${}_n{P}_r=\frac{n!}{\left(n-r\right)!}$ to evaluate ${}_6{P}_4$ .

Calculate the value of ${}_6{P}_4$ .

  $\begin{array}{c}{}_6{P}_4=\frac{6!}{\left(6-4\right)!}\\ =\frac{6\times 5\times 4\times 3\times 2!}{2!}\\ =6\times 5\times 4\times 3\\ =360\end{array}$

Therefore, the value of permutation ${}_6{P}_4$ is $360$ .