The number of distinct terms in the expansion of ${(x_{1} + x_{2} + . . . . . . + x_{n})}^{3}$ is

{^{n + 1} C}_{3}

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{^{n + 2} C}_{3}

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{^{n + 3} C}_{3}

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none of these

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Solution

The correct option is D ${^{n + 2} C}_{3}$
Consider
$(x_{1} + x_{2} + x_{3} . . . x_{r})^{n}$
Then the total number of distinct terms will be
$^{n + r - 1} C_{n}$
Replacing $r$ by $n$ and $n$ by $3$ , we get
Total number of distinct terms equal to
$^{3 + n - 1} C_{3}$
$=^{n + 2} C_{3}$

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Similar questions

The sum to (n+1) terms of the following series

$\frac{C_{0}}{2} - \frac{C_{1}}{3} + \frac{C_{2}}{4} - \frac{C_{3}}{5}$ + ......... is

\frac{C_{0}}{2} - \frac{C_{1}}{3} + \frac{C_{2}}{4} - \frac{C_{3}}{5} + \dots

(x_{1} + x_{2} + \dots . + x_{n})^{3}

n + 2 c_{3}

(2^{1 / 5} + 3^{1 / 10})^{55}

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{^{n} C}_{2} + {^{n} C}_{3} = {^{6} C}_{3}

{^{n} C}_{x} = {^{n} C}_{3}, x \neq 3

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^{(n + 1)} C_{3} -^{(n - 1)} C_{3} =

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