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Find n, if: `((17 - "n")!)/((14 - "n")!)` = 5!

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#### Solution

`((17 - "n")!)/((14 - "n")!)` = 5!

∴ `((17 - "n")(16 - "n")(15 - "n")(14 - "n")!)/((14 - "n")!)` = 5 × 4 × 3 × 2 × 1

∴ (17 – n) (16 – n) (15 – n) = 6 × 5 × 4

Comparing on both sides, we get

17 – n = 6

∴ n = 11

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