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Q.
The number of terms in the expansion of $(a + b + c)^{10}$ is
Binomial Theorem
Solution:
We have, $(a + b + c)^{10} = [a + (b + c)]^{10}$
$=\,{}^{10}C_{0}\,a^{10}+\,{}^{10}C_{1}\,a^{9}\left(b+c\right)+\,{}^{10}C_{2}\,a^{8} \left(b+c\right)^{2}+\ldots$
$\ldots +\,{}^{10}C_{10}\,\left(b+c\right)^{10}$
So, we can see that first term contains $1$ term, second term contains $2$ terms, $3^{rd}$ term contains $3$ terms and so on.
$\therefore $ Total number of terms in the given expansion
$= 1 + 2 + 3 + ... + 11$
$= \frac{11\left(11+1\right)}{2} = 66$