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If ^{n}P_{r} = 1680 and ^{n}C_{r} = 70, find n and r.

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#### Solution

Given that ^{n}P_{r} = 1680, ^{n}C_{r} = 70

We know that ^{n}C_{r} = `("nP"_"r")/("r"!)`

`70 = 1680/("r!")`

r! = `1680/70` = 24

r! = 4 × 3 × 2 × 1 = 4!

∴ r = 4

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