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