If (n + 2)! = 60 [(n − 1)!], find n.
Question:

If (n + 2)! = 60 [(n − 1)!], find n.

Solution:

(n + 2)! = 60 [(n − 1)!]

$\Rightarrow(n+2) \times(n+1) \times(n) \times(n-1) !=60[(n-1) !]$

$\Rightarrow(n+2) \times(n+1) \times(n)=60$

 

$\Rightarrow(n+2) \times(n+1) \times(n)=5 \times 4 \times 3$

∴ n = 3

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