Q.

Coefficient of  x4 in 1+x+x2+x311 is

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answer is 990.

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Detailed Solution

We have, 1+x+x2+x3=1+x+x2(1+x)=(1+x)1+x21+x+x2+x311=(1+x)111+x211=1+11C1x+11C2x2+11C3x3+11C4x4+…1+11C1x2+11C2x4+…Thus, coefficient of x4 in 1+x+x2+x311=(1) 11C2+ 11C2 11C1+ 11C4(1)=55+(55)(11)+330=990
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Coefficient of  x4 in 1+x+x2+x311 is