The number of terms after expansion in $(a + b + c)^{n}$ are:

n

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n^{2}

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\frac{(n + 1) (n + 2)}{2}

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\frac{n (n + 1)}{2}

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Solution

The correct option is D $\frac{(n + 1) (n + 2)}{2}$
Total no. of terms in ${(a_{1} + a_{2} + . . . + a_{n})}^{m}$ , where $a_{1}, a_{2} . . . a_{n}$ are independent variables is $^{m + n - 1} C_{n - 1}$
Hence, in ${(a + b + c)}^{n}$ , no. of terms is $^{n + 3 - 1} C_{3 - 1} =^{n + 2} C_{2} = \frac{(n + 1) (n + 2)}{2}$

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