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Question
If nPr = 720 and nCr = 120, find n, r
Solution
Given nPr = 720, If nCr = 120
`("n"!)/(("n" - "r")!)` = 720
`("n"!)/("r"!("n" - "r")!)` 120
`(("n"!)/(("n" - "r")!))/(("n"!)/("r"("n" - "r")!)) = 720/120`
`("n"!)/(("n" - "r")!) xx ("r"!("n" - "r")!)/("n"!)` = 6
r! = 6
r! = 3 × 2 × 1 = 3!
r = 3
Substituting r = 3 in `("n"!)/(("n" - "r")!)` = 720
`("n"!)/(("n" - 3)!)` = 720
`("n"("n" - 1)("n" - 2)("n" - 3)!)/(("n" - 3)!)` = 720
n (n – 1)(n – 2) = 720
n(n – 1)(n – 2) = 10 × 9 × 8
n = 10
∴ r = 3, n = 10
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