Question

Find the value of each permutation.

$P(7,2)$

Short answer

The value of the given permutation is 42.

Step-by-step solution

Step 1. Given information.

The given permutation is $P(7,2)$.

Step 2. Determine the value of the permutation.

We know that,

$P(n,r)=\frac{n!}{(n-r)!}$

The given permutation can be written as:

$\begin{array}{rcl}P(7,2)& =& \frac{7!}{(6-2)!}\\ & =& \frac{7!}{5!}\\ & =& \frac{7\times 6\times 5!}{5!}\\ & =& 7\times 6\\ & =& 42\end{array}$

Step 3. Conclusion.

The value of the given permutation is 42.