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The coefficient of x⁴ in the expansion of ${(1 + x + x^{2} + x^{3})}^{11}$ is

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Correct option is C

Let E=1+x+x2+x311=(1+x)1+x211=(1+x)111+x211General term of E is,T(r,k)= 11Crxr 11Ckx2k=11Cr⋅11Ckxr+2k For taking coefficient of x4 taker+2k=4 . Coefficient of x4 =T(0,2)+T(2,1)+T(4,0)=11C011C2+11C211C1+11C411C0=55+55×11+330=55+605+330=990

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The coefficient of x4 in the expansion of 1+x+x2+x311 is

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The coefficient of x⁴ in the expansion of ${(1 + x + x^{2} + x^{3})}^{11}$ is