Question

The co-efficient of \(a^{3} b^{4} c^{5}\) in the expansion of \((b c+c a+a b)^{6}\) is
(A) \(\frac{12 !}{3 ! 4 ! 5 !}\)
(B) \(\frac{6 !}{3 !}\)
(C) 33
(D) \(3 \cdot\left(\frac{6 !}{3 ! 3 !}\right)\)

Answer 1

Ans: (D)
Hint : \(\left\{\frac{6 !}{p ! q ! r !} a^{q+r} b^{p+r} c^{p+q}\right.\)
$$
\begin{aligned}
&q+r=3, p+r=4, p+q=5, p+q+r=6 \\
&\Rightarrow p=3, q=2, r=1
\end{aligned}
$$
co-efficient \(=\frac{6 !}{3 ! 2 !}\)