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If (N + 3)! = 56 [(N + 1)!], Find N.

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Question

If (n + 3)! = 56 [(n + 1)!], find n.

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Solution

(n + 3)! = 56 [(n + 1)!]

\[\Rightarrow\](n + 3)\[\times\] (n + 2)\[\times\](n + 1)! = 56 [(n + 1)!]
\[\Rightarrow\](n + 3)\[\times\](+ 2) = 56
\[\Rightarrow\] (n + 3)\[\times\] (n + 2) = 8\[\times\]7
\[\Rightarrow\] n + 3 = 8

∴ n = 5

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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 9 | Page 4

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