Question

Coefficient of $x^{11}$ in the expansion of
$(1+x^2{)}^4(1+x^3{)}^7(1+x^4{)}^{12}$ is

• A. 1051
• B. 1106
• C. 1113
• D. 1120

Answer 1

The correct option is C 1113

Choose Powers of x from each of the expansions such that they add up to 11.

${}^4{C}_4\times {}^7{C}_1\times {}^{12}{C}_0=7$

${}^4{C}_2\times {}^7{C}_1\times {}^{12}{C}_1=504$

${}^4{C}_1\times {}^7{C}_3\times {}^{12}{C}_0=140$

${}^4{C}_0\times {}^7{C}_1\times {}^{12}{C}_2=462$

Adding we get the answer as 1113 ways.