- Home
- Standard 11
- Mathematics
7.Binomial Theorem
normal
If $r,k,p \in W,$ then $\sum\limits_{r + k + p = 10} {{}^{30}{C_r} \cdot {}^{20}{C_k} \cdot {}^{10}{C_p}} $ is equal to -
A
$\left( {\begin{array}{*{20}{c}}
{60} \\
{50}
\end{array}} \right)$
B
$\left( {\begin{array}{*{20}{c}}
{60} \\
{30}
\end{array}} \right)$
C
$\left( {\begin{array}{*{20}{c}}
{60} \\
{20}
\end{array}} \right)$
D
$\left( {\begin{array}{*{20}{c}}
{30} \\
{10}
\end{array}} \right)\left( {\begin{array}{*{20}{c}}
{30} \\
{20}
\end{array}} \right)$
Solution
requind sum is coefficientof $x^{10}$ in the expansion of $(1+x)^{30}(1+x)^{20}(1+x)^{10}$ i.e. ${\,^{60}}{C_{10}}$
Standard 11
Mathematics
