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Question

If $$^nP_4=20\,^nP_2$$ find '$$n$$'


Solution

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

Mathematics

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