Chapter 0.4, Problem 6E

To determine

To find: Evaluate the permutation ${{\displaystyle P}}_5^7$ .

Answer to Problem 6E

2520.

Explanation of Solution

Given information: ${{\displaystyle P}}_5^7$

Formula used: ${{\displaystyle P}}_r^n=\frac{n!}{(n-r)!}$

Calculation:

Plug in the values of n and r into the formula.

  ${{\displaystyle P}}_5^7=\frac{7!}{(7-5)!}$

Simplify the right side,

  $=\frac{7!}{2!}$

  $=\frac{7*6*5*4*3*2!}{2!}$

Simplify it further,

  $=7*6*5*4*3$

  $=2520$

Hence ${{\displaystyle P}}_5^7=2520$