- Home
- Standard 11
- Mathematics
$\left( {_{\,4}^{47}} \right) + \sum\limits_{r = 1}^5 {\left( {_{\,\,\,\,3}^{52 - r}} \right)} = .........$
$\left( {\begin{array}{*{20}{c}}{47}\\6\end{array}} \right)$
$\left( {\begin{array}{*{20}{c}}{52}\\5\end{array}} \right)$
$\left( {\begin{array}{*{20}{c}}{52}\\4\end{array}} \right)$
$\left( {\begin{array}{*{20}{c}}{52}\\3\end{array}} \right)$
Solution
$\left( {\begin{array}{*{20}{c}}
{47} \\
4
\end{array}} \right) + \sum\limits_{r = 1}^5 {\left( {\begin{array}{*{20}{c}}
{52 – r} \\
3
\end{array}} \right)} $
$ = \left( {\begin{array}{*{20}{c}}
{51} \\
3
\end{array}} \right) + \left( {\begin{array}{*{20}{c}}
{50} \\
3
\end{array}} \right) + \left( {\begin{array}{*{20}{c}}
{49} \\
3
\end{array}} \right) + \left( {\begin{array}{*{20}{c}}
{48} \\
3
\end{array}} \right) + \left( {\begin{array}{*{20}{c}}
{47} \\
4
\end{array}} \right)$
$\left( {\begin{array}{*{20}{c}}
{51} \\
3
\end{array}} \right) + \left( {\begin{array}{*{20}{c}}
{50} \\
3
\end{array}} \right) + \left( {\begin{array}{*{20}{c}}
{49} \\
3
\end{array}} \right) + \left( {\begin{array}{*{20}{c}}
{48} \\
3
\end{array}} \right) + \left( {\begin{array}{*{20}{c}}
{48} \\
4
\end{array}} \right)$
$ = \left( {\begin{array}{*{20}{c}}
{51} \\
3
\end{array}} \right) + \left( {\begin{array}{*{20}{c}}
{50} \\
3
\end{array}} \right) + \left( {\begin{array}{*{20}{c}}
{49} \\
3
\end{array}} \right) + \left( {\begin{array}{*{20}{c}}
{49} \\
4
\end{array}} \right)$
$\left( {\begin{array}{*{20}{c}}
{51} \\
3
\end{array}} \right) + \left( {\begin{array}{*{20}{c}}
{50} \\
3
\end{array}} \right) + \left( {\begin{array}{*{20}{c}}
{50} \\
4
\end{array}} \right)$
$ = \left( {\begin{array}{*{20}{c}}
{51} \\
3
\end{array}} \right) + \left( {\begin{array}{*{20}{c}}
{51} \\
4
\end{array}} \right) = \left( {\begin{array}{*{20}{c}}
{52} \\
4
\end{array}} \right)$
