Question

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

• A. 13
• B. 39
• C. 78
• D. 91

Answer 1

Answer: (D)

$(a+b+c{)}^{12}=[(a+b)+c{]}^{12}$
$={}^{12}{C}_0(a+b{)}^{12}+{}^{12}{C}_1(a+b{)}^{11}c+\dots +{}^{12}{C}_{12}{c}^{12}$
The $R.H.S$. contains, $13+12+11+\dots .+1$ 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 $n=12;{}^{n+2}{C}_2={}^{14}{C}_2=\frac{14\times 13}{2}=91$