Find the value of ${}^{8}{P_{8}}$

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Solution

Compute the required value
Given expression is ${}^{8}P_{8}$
We know that ${}^{n}P_{r} = \frac{n!}{(n - r)!}$
$\Rightarrow {}^{8}P_{8} = \frac{8!}{(8 - 8)!} = \frac{8!}{0!}$
$\Rightarrow$ $= 8!$ $. . . (∵ 0! = 1)$
$\Rightarrow$ ${}^{8}{P_{8}} = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 40320$
Hence the value of ${}^{8}P_{8}$ is $40320$

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