Mathematics - Binomial Theorem Question with Solution | TestHub

$2x_1+3x_2+4x_3=11$
Possibilities are$\left(0, 1, 2\right);\left(1, 3, 0\right);\left(2, 1, 1\right);\left(4, 1, 0\right)$
$\therefore$Required coefficients
$=\left({ }^4{C}_0\times { }^7{C}_1\times { }^{12}{C}_2\right)+\left({ }^4{C}_1\times { }^7{C}_3\times { }^{12}{C}_0\right)+\left({ }^4{C}_2\times { }^7{C}_1\times { }^{12}{C}_1\right)+({ }^4{C}_4\times { }^7{C}_1\times 1)$
$=\left(1\times 7\times 66\right)+\left(4\times 35\times 1\right)+\left(6\times 7\times 12\right)+\left(1\times 7\right)$
$=462+140+504+7=1113$