If $^{n} P_{r} = 840,^{n} C_{r} = 35$ .Find r.

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Solution

$^{n} P_{r} = 840^{n} C_{r} = 35 \Rightarrow d \frac{^{n} P_{r}}{r!} =^{n} C_{r} \Rightarrow \frac{840}{35} = r! \Rightarrow r! = 24 \Rightarrow r! = 4! \Rightarrow r = 4$
Hence the correct answer is $4$

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