Q97 / 155 · WBJEE 2021 · Mathematics

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
  • Correct answer
    D
    3. $\left(\frac{6 !}{3 ! 3 !}\right)$

Solution

$\left\{\frac{6 !}{p ! q ! r !} a^{q+r} b^{p+r} c^{p+q}\right.$ $q+r=3, p+r=4, p+q=5, p+q+r=6$ $\Rightarrow p=3, q=2, r=1$ co-efficient $=\frac{6 !}{3 ! 2 !}$

Hence, the correct answer is option: 'D'.

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