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) $\times$ (n + 2) = 56
$\Rightarrow$ (n + 3) $\times$ (n + 2) = 8 $\times$ 7
$\Rightarrow$ n + 3 = 8
∴ n = 5

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