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Permutations — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSPermutations3 Marks
Question
If (n + 2)! = 60 [(n - 1)!], find n.
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Answer

We have,(n + 2)! = 60 [(n - 1)!]
(n + 2) (n + 1) (n) (n - 1)! = 60 [(n - 1)!]
$\Rightarrow (\text{n}-2) (\text{n}+1)\text{n}= 5\times 4\times3 $ [By comparing] $\therefore \text{n}= 3$ Hence, n = 3

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