If 2.P(5,3) = P(n,4), Find n.

Dear student

We have, 2 . P (5, 3) = P (n, 4) \Rightarrow P (n, 4) = 2 P (5, 3) \Rightarrow \frac{n!}{(n - 4)!} = 2 (\frac{5!}{(5 - 3)!}) \Rightarrow \frac{n (n - 1) (n - 2) (n - 3) (n - 4)!}{(n - 4)!} = \frac{2 (5!)}{2!} \Rightarrow n (n - 1) (n - 2) (n - 3) = 5! \Rightarrow n (n - 1) (n - 2) (n - 3) = 5 \times 4 \times 3 \times 2 \times 1 \Rightarrow n (n - 1) (n - 2) (n - 3) = 5 . (5 - 1) . (5 - 2) . (5 - 3) \Rightarrow n = 5 (By comparing two sides)

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