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Home  >>  CBSE XI  >>  Math  >>  Binomial Theorem

The number of terms in the expansion of $(a+b+c)^{10}$ is

$\begin{array}{1 1}(A)\;11\\(B)\;21\\(C)\;55\\(D)\;66\end{array} $

1 Answer

Toolbox:
  • $(a+b)6n=nC_0a^nb^0+nC_1a^{n-1}b^2.......nC_na^0b^n$
$(a+b+c)^{10}=(a+(b+c))^{10}$
$\Rightarrow 10C_0a^{10}(b+c) ^0+10C_1a^9(b+c)^2+.....10C_{10}a^0(b+c)^{10}$
$\therefore$ No of terms in $(a+b+c)^{10}$
$\Rightarrow 1+2+3+.....11$
$\Rightarrow \large\frac{11}{2}$$(2(1)+(11-1).1)$
$\Rightarrow 66$
Hence (D) is the correct answer.
answered Jun 26, 2014 by sreemathi.v
 

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