If $^{n} P_{4} = 20^{n} P_{2}$ find ' $n$ '

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Solution

$^{n} P_{4} = 20^{n} P_{2} \Rightarrow \frac{n!}{(n - 4)!} = 20 \frac{n!}{(n - 2)!} \Rightarrow (n - 3) (n - 2) = 5 \times 4 \Rightarrow n = 7$
Hence the correct answer is $7$

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