Maharashtra State BoardHSC Science (General) 11th
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Find n, if: n!3!(n-3)!:n!5!(n-7)! = 1 : 6 - Mathematics and Statistics

Sum

Find n, if: `("n"!)/(3!("n" - 3)!) : ("n"!)/(5!("n" - 7)!)` = 1 : 6

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Solution

`("n"!)/(3!("n" - 3)!) : ("n"!)/(5!("n" - 7)!)` = 1 : 6

∴ `("n"!)/(3!("n" - 3)!) xx (5!("n" - 7)!)/("n"!) = 1/6`

∴ `(5!("n" -  7)!)/(3!("n" - 3)!) = 1/6`

∴ `(5 xx 4 xx 3! xx ("n" - 7)!)/(3! xx ("n" - 3)("n" - 4)("n" - 5)("n" - 6)("n" - 7)!) = 1/6`

∴ `(5 xx 4)/(("n" - 3)("n" - 4)("n" - 5)("n" - 6)) =1/6`

∴ (n – 3)(n – 4)(n – 5)(n – 6) = 6 × 5 × 4

∴ (n – 3)(n – 4)(n – 5)(n – 6) = 5 × 4 × 3 × 2

∴ (n – 3)(n – 4)(n – 5)(n – 6) = (8 – 3)(8 – 4)(8 – 5)(8 – 6)

∴ n = 8

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APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 3 Permutations and Combination
Exercise 3.2 | Q 6. (iv) | Page 50
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