Let r and n be positive integers such that 1≤ r ≤ n. Then prove the following nCr/ (n-1)C(r-1) = n/r

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Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove : n(n-1)C(r-1)=(n-r + 1) nC(r-1)

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Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove: nCr +2 nC(r-1) + nC(r-2) = (n+2)Cr

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Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following: nCr/nCr-1 = n-r+1/n