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બે મિત્રોમાં $12$ દડા.....પ્રકારે વહેચાય કે જેથી એકને $8$ દડા તથા બીજાને દડા $4 $ મળે.
$\,\frac{{12\,!}}{{8\,!\,4\,!}}$
$\,\frac{{2\,!\,12\,!}}{{8\,!\,4\,!}}$
$\,\frac{{\,12\,!}}{{8\,!\,4\,!2\,!}}$
આમાંથી કોઇપણ નહી.
Solution
દડા વહેચવાના પ્રકાર
$ = \,\,\left( {\begin{array}{*{20}{c}}
{12} \\
8
\end{array}} \right)\,\,\left( {\begin{array}{*{20}{c}}
4 \\
4
\end{array}} \right)\,\, + \,\,\left( {\begin{array}{*{20}{c}}
{12} \\
4
\end{array}} \right)\,\,\left( {\begin{array}{*{20}{c}}
8 \\
8
\end{array}} \right)\,\,\, = \,\,\left( {\begin{array}{*{20}{c}}
{12} \\
8
\end{array}} \right)\,\,\, + \,\,\left( {\begin{array}{*{20}{c}}
{12} \\
4
\end{array}} \right)\,\,\, = \,\,\left( {\begin{array}{*{20}{c}}
{12} \\
8
\end{array}} \right)\,\, + \,\,\left( {\begin{array}{*{20}{c}}
{12} \\
8
\end{array}} \right)\,$
$\,\, = \,2\,\,.\,\,\frac{{12\,!}}{{8\,!\,4\,!}}\,\,\, $
$= \,\,\frac{{2\,!\,12\,!}}{{8\,!\,4\,!}}$
