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$\left( {\,_{15}^{18}\,} \right) + 2\left( {\,_{16}^{18}\,} \right) + \left( {\,_{16}^{17}\,} \right) + 1 = \left( {_{\,3}^{\,n}\,} \right),\,$, હોય ,તો $\,{\text{n = }}...........$
$18$
$19$
$20$
$24$
Solution
$\left( {\begin{array}{*{20}{c}}
n \\
{r – 1}
\end{array}} \right) + \left( {\begin{array}{*{20}{c}}
n \\
r
\end{array}} \right) = \left( {\begin{array}{*{20}{c}}
{n + 1} \\
r
\end{array}} \right)$ મળે
અહી $ \left( {\begin{array}{*{20}{c}}
{18} \\
{15}
\end{array}} \right) + \left( {\begin{array}{*{20}{c}}
{18} \\
{16}
\end{array}} \right) + \left( {\begin{array}{*{20}{c}}
{18} \\
{16}
\end{array}} \right) + \left( {\begin{array}{*{20}{c}}
{17} \\
{16}
\end{array}} \right) + \left( {\begin{array}{*{20}{c}}
{17} \\
{17}
\end{array}} \right) = \left( {\begin{array}{*{20}{c}}
n \\
3
\end{array}} \right)$
$\left( {\begin{array}{*{20}{c}}
{19} \\
{16}
\end{array}} \right)\, + \left( {\begin{array}{*{20}{c}}
{18} \\
{16}
\end{array}} \right) + \left( {\begin{array}{*{20}{c}}
{18} \\
{17}
\end{array}} \right) = \left( {\begin{array}{*{20}{c}}
n \\
3
\end{array}} \right)\,\,$
$\left( {\begin{array}{*{20}{c}}
{19} \\
{16}
\end{array}} \right) + \left( {\begin{array}{*{20}{c}}
{19} \\
{17}
\end{array}} \right) = \left( {\begin{array}{*{20}{c}}
n \\
3
\end{array}} \right)\,$
$\,\left( {\begin{array}{*{20}{c}}
{20} \\
{17}
\end{array}} \right) = \left( {\begin{array}{*{20}{c}}
n \\
{n – 3}
\end{array}} \right)$
$n\,\, = \,\,20$ મળે
