Question

Evaluate each expression

$P\left(6,3\right)$

Short answer

The value of $P\left(6,3\right)=120$.

Step-by-step solution

Step 1. Given Information.

Given to evaluate the expression $P\left(6,3\right)$.

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=6,r=3

Plugging the values:

$\begin{array}{l}P\left(6,3\right)=\frac{6!}{\left(6-3\right)!}\\ P\left(6,3\right)=\frac{6!}{3!}\\ P\left(6,3\right)=\frac{6\cdot 5\cdot 4\cdot 3!}{3!}\\ P\left(6,3\right)=6\cdot 5\cdot 4\cdot \\ P\left(6,3\right)=120\end{array}$

Step 3. Conclusion.

Hence, the value of $P\left(6,3\right)=120$