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Find n, if: nn(15-n)!(13-n)! = 12

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Question

Find n, if: `((15 - "n")!)/((13 - "n")!)` = 12

Sum
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Solution

`((15 - "n")!)/((13 - "n")!)` = 12

∴ `((15 - "n")(14 - "n")(13 - "n")!)/((13 - "n")!)` = 12

∴ (15 – n) (14 – n) = 4 × 3

Comparing on both sides, we get

∴ 15 – n = 4

∴ n = 11

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Chapter 3: Permutations and Combination - Exercise 3.2 [Page 49]

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