Find n, if: (17-n)!(14-n)! = 5! - Mathematics and Statistics

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Sum

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

Concept: Concept of Factorial Function
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Chapter 6: Permutations and Combinations - Exercise 6.2 [Page 76]

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Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Exercise 6.2 | Q 9. (i) | Page 76
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