Find the coefficient of $a^{3} b^{3} c$ in the expansion ${(2 a + b + 3 c)}^{7}$

3360

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3361

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3300

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3330

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Solution

The correct option is D $3360$
The formula to find the coefficient of $x^{p} y^{q} z^{r}$ in $(a x + b y + c z)^{n}$ is $\frac{n! a^{p} b^{q} c^{r}}{p! q! r!}$
So, coefficient of $a^{3} b^{3} c$ in $(2 a + b + 3 c)^{7} = \frac{7! 2^{3} 1^{3} 3^{1}}{3! 1! 3!}$ =3360

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