Question

Evaluate each expression

$P\left(7,5\right)$

Short answer

The value of $P\left(7,5\right)=2520$.

Step-by-step solution

Step 1. Given Information.

Given to evaluate the expression $P\left(7,5\right)$.

Step 2. Calculation.

When n objects are available and r are to be picked then the number of permutations is given by $P\left(n,r\right)=\frac{n!}{\left(n-r\right)!}$

Here n=7,r=5

Plugging the values:

$\begin{array}{l}P\left(7,5\right)=\frac{7!}{\left(7-5\right)!}\\ P\left(7,5\right)=\frac{7!}{2!}\\ P\left(7,5\right)=\frac{7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2!}{2!}\\ P\left(7,5\right)=7\cdot 6\cdot 5\cdot 4\cdot 3\\ P\left(7,5\right)=2520\end{array}$

Step 3. Conclusion.

Hence, the value of $P\left(7,5\right)=2520$.