Find the value of $^{7} P_{3}$

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Solution

We know that:
$^{n} P_{r} = \frac{n!}{(n - r)!}$
$∴^{7} P_{3} = \frac{7!}{(7 - 3)!} = \frac{7!}{4!} = \frac{7 \times 6 \times 5 \times 4!}{4!} = 7 \times 6 \times 5 = 210$
Hence, $^{7} P_{3} = 210$

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