$\left( {\begin{array}{*{20}{c}}
  n \\ 
  0 
\end{array}} \right) + \left( {\begin{array}{*{20}{c}}
  n \\ 
  1 
\end{array}} \right) + \left( {\begin{array}{*{20}{c}}
  n \\ 
  2 
\end{array}} \right) + …. + \left( {\begin{array}{*{20}{c}}
  n \\ 
  n 
\end{array}} \right) = {2^n}$

$6$ પુસ્તકોમાંથી  $1, 2, 3, 4, 5$ કે $6$ પુસ્તકોની પસંદગી

$\left( {\begin{array}{*{20}{c}}
  6 \\ 
  1 
\end{array}} \right) + \left( {\begin{array}{*{20}{c}}
  6 \\ 
  2 
\end{array}} \right) + \left( {\begin{array}{*{20}{c}}
  6 \\ 
  3 
\end{array}} \right) + \left( {\begin{array}{*{20}{c}}
  6 \\ 
  4 
\end{array}} \right) + \left( {\begin{array}{*{20}{c}}
  6 \\ 
  5 
\end{array}} \right) + \left( {\begin{array}{*{20}{c}}
  6 \\ 
  6 
\end{array}} \right)$

$ = {2^6} – 1 = 64 – 1 = 63$