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Question

n1r=0nCrnCr+nCr+1 is equal to

A
n2
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B
n+12
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C
n(n+1)2
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D
n(n1)2(n+1)
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Solution

The correct option is A n2
n1r=0nCrnCr+nCr+1

=n1r=0nCrn+1Cr+1 ----------(because nCr+nCr1=n+1Cr)

=n1r=0nCr(n+1)(r+1)nCr

=n1r=0r+1n+1

=n(n+1)2(n+1)

=n2

hence option A is correct.





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