Question

Evaluate the expression.

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

Short answer

The value of the expression$P\left(6,3\right)$ is 120.

Step-by-step solution

Step 1. Define permutation.

When the objects are arranged so that order is important and every possible order of the objects is provided, the arrangements is called a permutation.

Step 2. Define the meaning of Pn, r.

The number of permutations of r objects taken from the group of n objects is given by

$P\left(n,r\right)=\frac{n!}{\left(n-r\right)!}\mathrm{............}\left(1\right)$

Step 3. Evaluate the expression P6, 3.

Use equation (1) to evaluate the expression $P\left(6,3\right)$.

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

Therefore, the value of the expression$P\left(6,3\right)$ is 120.