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$Coefficient of x^{6} in (1 + x) {(1 + x^{2})}^{2} {(1 + x^{3})}^{3} ........ {(1 + x^{n})}^{n}, n \geq 6, is$

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Correct option is B

The coefficient of x6 in the given expression= Coefficient of x6 in 1+6C1x61+5C1x51+4C1x41+3C1x3+3C2x61+2C1x2+2C2x4(1+x)= Coefficient of x6 in 1+6x6+5x5+4x41+2x2+3x3+x4+6x5+3x61+x= Coefficient of x6 in 11x5+17x6(1+x)=28

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Coefficient of x6 in (1+x)1+x221+x33 ........ 1+xnn,n≥6 , is

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$Coefficient of x^{6} in (1 + x) {(1 + x^{2})}^{2} {(1 + x^{3})}^{3} ........ {(1 + x^{n})}^{n}, n \geq 6, is$