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Question

Prove that nCr+nCr1=n+1Cr.

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Solution

Now,
nCr+nCr1
=n!r!(nr)!+n!(r1)!(nr+1)! [ Using the definition of nCr]
=n!(nr)!(r1)![1r+1(nr+1)]
=n!(nr)!(r1)![(n+1)r(n+1r)]
=(n+1)!r!(n+1r)!
=n+1Cr.

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