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प्रश्न
Find n, if: `("n"!)/(3!("n" - 3)!) : ("n"!)/(5!("n" - 5)!)` = 5 : 3
उत्तर
`("n"!)/(3!("n" - 3)!) : ("n"!)/(5!("n" - 5)!)` = 5 : 3
∴ `("n"!)/(3!("n" - 3)!) xx (5!("n" - 5)!)/("n"!) = 5/3`
∴ `("n"!)/(3!("n" - 3)("n" - 4)("n" - 5)!) xx (5 xx 4 xx 3!("n" - 5)!)/("n"!) = 5/3`
∴ `(5 xx 4)/(("n" - 3)("n" - 4)) = 5/3`
∴ 12 = (n – 3)(n – 4)
∴ (n – 3)(n – 4) = 4 × 3
Comparing on both sides, we get
n – 3 = 4
∴ n = 7
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