The coefficient of $x^{40}$ in $(1 + 3 x + 3 x^{2} + x^{3})^{20}$ , is:

^{60} C_{40}

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^{30} C_{20}

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^{15} C_{2}

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0

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Solution

The correct option is A $^{60} C_{40}$
We know ${(1 + x)}^{3} = 1 + 3 x + 3 x^{2} + x^{3}$
So, we need to find coefficent of $x^{40}$ in the expansion of ${(1 + x)}^{60}$
The genral term can be written as $T_{r + 1}$ = $^{n} C_{r} . x^{r}$
So we put r=40
Hence, coefficent of $x^{40}$ is $^{60} C_{40}$

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