Value of $r$ when $^{20} P_{r}$ attains maximum value is

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Solution

$^{20} P_{r} ⟶$ maximum value
$\Rightarrow^{n} P_{r} = \frac{n!}{(n - r)!}$
It has maximum value when $(20 - r)!$ is least
$\Rightarrow 20 - r$ is least
= possible value of $20 - r = 0$
$r = 20$
At $r =$ $^{20} P_{r}$ is maximum
Hence the correct answer is $r = 20$

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