The value of ${}^{20}{P_{2}}$ is ?

$20$

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$19$

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$380$

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None of these

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Solution

The correct option is C
$380$

Explanation for the correct answer:
The formula for ${}^{n}{P_{r}}$ is given as
${}^{n}{P_{r}} = \frac{n!}{(n - r)!}$
Here we have, $n = 20, r = 2$
$\Rightarrow$ ${}^{20}{P_{2}} = \frac{20!}{(20 - 2)!}$
$\Rightarrow$ ${}^{20}{P_{2}} = \frac{20!}{18!}$
$\Rightarrow$ ${}^{20}{P_{2}} = 20 \times 19$
$\Rightarrow$ ${}^{20}{P_{2}} = 380$
Hence, the value of ${}^{20}{P_{2}}$ is $380$ , so correct option is (C).

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