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Question

If (1+x)n=C0+C1x+C2x2++Cnxn, then 0r<sn(r+s)(Cr+Cs+CrCs) is equal to

A
n22nn2[22n 2nCn]
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B
n22n+n2[22n 2nCn]
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C
n22n+n2[22n+ 2nCn]
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D
None of these
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Solution

The correct option is B n22n+n2[22n 2nCn]
We have,
0r<sn(r+s)(Cr+Cs+CrCs)=0r<sn(r+s)(Cr+Cs)+0r<sn(r+s)CrCs

=n22n+n2[22n 2nCn]

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