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The coefficient of $x^{4}$ in the expansion ${(1 + x + x^{2} + x^{3})}^{6}$ in power of $x$ is

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Correct option is A

We have , 1+x+x2+x36=(1+x)61+x26 =∑r=06 6Crx5∑s=06 6Csx2s= 6C0+6C1x+6C2x2+6C3x3+6C4x4+…x 6C0+6C1x2+6C2x4+…∴ Coefficient of x4 in 1+x+x2+x36= 6C0×6C2+6C2×6C1+6C4×6C0 =15+ 90+15 =120

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The coefficient of x 4 in the expansion 1+x+x2+x36 in power of x is

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The coefficient of $x^{4}$ in the expansion ${(1 + x + x^{2} + x^{3})}^{6}$ in power of $x$ is