Question

Find the value of each permutation.

$P(8,4)$

Short answer

The value of the given permutation is 1680.

Step-by-step solution

Step 1. Given information.

The given permutation is $P(8,4)$.

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:

$\begin{array}{rcl}P(8,4)& =& \frac{8!}{(8-4)!}\\ & =& \frac{8!}{4!}\\ & =& \frac{8\times 7\times 6\times 5\times 4!}{4!}\\ & =& 8\times 7\times 6\times 5=1680\end{array}$

Step 3. Conclusion.

The value of the given permutation is 1680.