Chapter 11, Problem 10CT

To determine

To evaluate the given permutation

Answer to Problem 10CT

The given permutation is evaluated as,

  ${}_5{P}_2=60$

Explanation of Solution

Given information:the permutation is given as,

  ${}_5{P}_2$

Calculation: the given permutation can be evaluated as,

  $\begin{array}{l}{}_5{P}_2=\frac{5!}{\left(5-3\right)!}\left[\text{use permutation formula}\right]\\ {}_5{P}_2=\frac{5!}{2!}\left[\text{subtract}\right]\\ {}_5{P}_2=\frac{5\cdot 4\cdot 3\cdot 2\cdot 1}{2\cdot 1}\left[\text{expand factorials}\right]\\ {}_5{P}_2=5\cdot 4\cdot 3\left[\text{divide out common factor}\right]\\ {}_5{P}_2=60\left[\text{multiply}\right]\end{array}$

Therefore,

The given permutation is evaluated as,

  ${}_5{P}_2=60$