English

If (N + 2)! = 60 [(N − 1)!], Find N.

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Question

If (n + 2)! = 60 [(n − 1)!], find n. 

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Solution

(n + 2)! = 60 [(n − 1)!]

\[\Rightarrow\](n + 2)\[\times\](n + 1)\[\times\](n)\[\times\]( 1)! = 60 [(n − 1)!]
\[\Rightarrow\](n + 2)\[\times\](n + 1)\[\times\](n) = 60
\[\Rightarrow\](n + 2)\[\times\](n + 1)\[\times\](n) = 5\[\times\]4\[\times\]3

∴ n = 3


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Factorial N (N!) Permutations and Combinations
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Chapter 16: Permutations - Exercise 16.1 [Page 4]

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R.D. Sharma Mathematics [English] Class 11
Chapter 16 Permutations
Exercise 16.1 | Q 7 | Page 4

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