In the expression of $(a + b)^{n}$ there are n + 1 dissimilar terms. The number of dissimilar terms in the expansion of $(a + b + c)^{10}$ is:

11

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33

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55

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66

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Solution

The correct option is B $66$
$(a + b)^{n}$ has $(n + 1)$ dissimilar terms.
${(a + b + c)}^{10} = {(a + b)}^{10} +^{10} C_{1} {(a + b)}^{9} c + - - - - - - +^{10} C_{9} (a + b) c^{9} + C^{10} = 11 + 10 + 9 + - - - - - - + 1 (d i s s i m i l a r t e r m s) = \frac{11 (12)}{2} (d i s s i m i l a r t e r m s) = 66 (d i s s i m i l a r t e r m s)$

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