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Q.
The number of dissimilar terms in the expansion of $( a +$
b) $^{n}$ is $n+1$, therefore number of dissimilar terms in the expansion of $(a+b+c)^{12}$ is
Binomial Theorem
Solution:
$(a+b+c)^{12}=[(a+b)+c]^{12}$
$={ }^{12} C_{0}(a+b)^{12}+{ }^{12} C_{1}(a+b)^{11} c+\ldots+{ }^{12} C_{12} c^{12}$
The $R.H.S$. contains, $13+12+11+\ldots .+1$ terms
$=\frac{13(13+1)}{2}=91$ terms
Also no. of term in the expansion of $(a+b+c)^{n}$ is given by ${ }^{n+2} C_{2}$
Thus for $n =12 ;{ }^{ n +2} C _{2}={ }^{14} C _{2}=\frac{14 \times 13}{2}=91$