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Find n if: n!3!(n-5)!:n!5!(n-7)! = 10:3 - Mathematics and Statistics

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Sum

Find n if: `("n"!)/(3!("n" - 5)!) : ("n"!)/(5!("n" - 7)!)` = 10:3

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Solution

`("n"!)/(3!("n" - 5)!) : ("n"!)/(5!("n" - 7)!)` = 10:3

∴ `("n"!)/(3!("n" - 5)!)xx(5!("n" - 7)!)/("n"!) = 10/3`

`∴("n"!)/(3!("n"-5)("n"-6)("n"-7)!)xx(5xx4xx3!("n"-7)!)/("n"!)=10/3`
∴ `(5xx4)/(("n" - 5)("n" - 6)) = 10/3`
∴ (n – 5) (n – 6) = 3 × 2
Comparing on both sides, we get
∴ n – 5 = 3
∴ n = 8

Concept: Concept of Factorial Function
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Exercise 6.2 | Q 8. (ii) | Page 76
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