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If $^{n} P_{r} = 1680$ and $^{n} C_{r} = 70$ then $n$ is equal to

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Correct option is C

nPr=(r!) nCr⇒1680=(r!)(70)⇒r!=24⇒r=4Also 1680=nP4=n(n−1)(n−2)(n−3)⇒n2−3nn2−3n+2=1680⇒n2−3n+12=412⇒n2−3n+1=41⇒n2−3n−40=0⇒(n+5)(n−8)=0⇒n=8.

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If nPr=1680 and nCr=70 then n is equal to

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If $^{n} P_{r} = 1680$ and $^{n} C_{r} = 70$ then $n$ is equal to