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If $0 < r < s \leq n$ and $^{n} P_{r} =^{n} P_{s}$ then value of $r + s$ is

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2n−2

2n – 1

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Correct option is B

nPr=nPs⇒ n!(n−r)!=n!(n−s)!⇒ (n−r)!=(n−s)!As rn−s But the only two different factorials which are equal are 0! and 1! Thus n – r = 1 and n – s = 0 ⇒r=n−1 and s=n.⇒ r+s=2n−1.

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If 0<r<s≤n and nPr=nPs then value of r + s is

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If $0 < r < s \leq n$ and $^{n} P_{r} =^{n} P_{s}$ then value of $r + s$ is