$\left( {\begin{array}{*{20}{c}}
  {2n} \\ 
  3 
\end{array}} \right)\,\,:\,\,\left( {\begin{array}{*{20}{c}}
  n \\ 
  2 
\end{array}} \right)\, = \,44\,:3$

$\frac{{(2n)\,!}}{{3\,!\,(2n – 3)\,!}}.\,\frac{{2\,!(n – 2)\,!}}{{n\,!}} = \frac{{44}}{3}\,\,\,$

$\frac{{2n.(2n – 1)(2n – 2)(2n – 3)\,!}}{{3 \times 2(2n – 3)\,!}}.\frac{{2\,!(n – 2)\,!}}{{n(n – 1)(n – 2)\,!}} = \frac{{44}}{3}\,\,\,$

$\frac{{4(2n – 1)}}{3} = \frac{{44}}{3}\,\,$

$2n – 1 = 11$

$n =  = 6$

$\left( {\begin{array}{*{20}{c}}
  n \\ 
  r 
\end{array}} \right)\, = \,\left( {\begin{array}{*{20}{c}}
  6 \\ 
  r 
\end{array}} \right) = 15\,$ પણ $\left( {\begin{array}{*{20}{c}}
  6 \\ 
  2 
\end{array}} \right)\, = \,\left( {\begin{array}{*{20}{c}}
  6 \\ 
  4 
\end{array}} \right) = 15$

$r = 2$ કે $r = 4$ અહીં, $r = 4$ આપેલ છે