If P (n, 5) = 20. P(n, 3), find n

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Solution

P (n, 5) = 20. P(n, 3)
$\Rightarrow \frac{n!}{(n - 5)!} = 20 \times \frac{n!}{(n - 3)!} \Rightarrow \frac{n!}{n!} = 20 \times \frac{(n - 5)!}{(n - 3)!} \Rightarrow 1 = 20 \times \frac{(n - 5)!}{(n - 3) (n - 4) (n - 5)!} \Rightarrow (n - 3) (n - 4) = 20 \Rightarrow (n - 3) (n - 4) = 5 \times 4 On comparing the two sides, we get : \Rightarrow n - 3 = 5 \Rightarrow n = 8$

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