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Question
If `""^"n""P"_"r" = 1814400` and `""^"n""C"_"r"` = 45, find r.
Solution
`""^"n""P"_"r"` = 1814400, `""^"n""C"_"r"` = 45
∴ `(""^"n""P"_"r")/(""^"n""C"_"r")=1814400/45`
∴ `("n"!)/(("n" - "r")!)xx("r"!("n" - "r")!)/("n"!)=1814400/45`
∴ r! = 40320
∴ r! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
∴ r! = 8!
∴ r = 8
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