Q. The coefficient of $a^{5}b^{6}c^{7}$ in the expansion of ${(bc + ca + ab)}^{9}$ is
A) 100
B) 120
C) 720
D) 1260
Explanation
(d)
$(bc + ca + ab)^{9} = \lbrack{bc + a(b + c)\rbrack}^{9}$
$\therefore$ Coefficient of $a^{5}b^{6}c^{7}$
$\ =$ coefficient of $a^{5}b^{6}c^{7}$ in $\ ^{9}C_{5}(bc)^{4}a^{5}(b + c)^{5}$
=coefficient of $b^{2}c^{3}\ in\ \ ^{9}C_{5}(b + c)^{5}$
$= \ ^{9}C_{5} \times \ ^{5}C_{3} = 1260$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.