English
Hindi
6.Permutation and Combination
medium

$\left( {\begin{array}{*{20}{c}}{50}\\4\end{array}} \right)\,\, + \,\,\sum\limits_{i = 1}^6 {\left( {\begin{array}{*{20}{c}}{56\, - \,i}\\3\end{array}} \right)} = ......$

A

$\left( {\begin{array}{*{20}{c}}{55}\\4\end{array}} \right)$

B

$\left( {\begin{array}{*{20}{c}}{55}\\3\end{array}} \right)$

C

$\left( {\begin{array}{*{20}{c}}{56}\\3\end{array}} \right)$

D

$\left( {\begin{array}{*{20}{c}}{56}\\4\end{array}} \right)$

Solution

$\left( {\begin{array}{*{20}{c}}
  {50} \\ 
  4 
\end{array}} \right)\,\, + \,\,\sum\limits_{i = 1}^6 {\left( {\begin{array}{*{20}{c}}
  {56\, – \,i} \\ 
  3 
\end{array}} \right)}  = \,\,\left( {\begin{array}{*{20}{c}}
  {50} \\ 
  4 
\end{array}} \right)\,\, + \,\,$

$\left( {\begin{array}{*{20}{c}}
  {55} \\ 
  3 
\end{array}} \right)\,\, + \,\,\left( {\begin{array}{*{20}{c}}
  {54} \\ 
  3 
\end{array}} \right)\,\, + \,\,\left( {\begin{array}{*{20}{c}}
  {53} \\ 
  3 
\end{array}} \right)\,\, + \,\,\left( {\begin{array}{*{20}{c}}
  {52} \\ 
  3 
\end{array}} \right)\,\, + \,\left( {\begin{array}{*{20}{c}}
  {51} \\ 
  3 
\end{array}} \right)\,\, + \,\,\left( {\begin{array}{*{20}{c}}
  {50} \\ 
  3 
\end{array}} \right)$

$ = \,\,\left( {\begin{array}{*{20}{c}}
  {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}}
  {52} \\ 
  3 
\end{array}} \right)\,\, + \,\,\left( {\begin{array}{*{20}{c}}
  {53} \\ 
  3 
\end{array}} \right)\,\, + \,\,\left( {\begin{array}{*{20}{c}}
  {54} \\ 
  3 
\end{array}} \right)\,\, + \,\,\left( {\begin{array}{*{20}{c}}
  {55} \\ 
  3 
\end{array}} \right)$

$ = \,\,\left( {\begin{array}{*{20}{c}}
  {51} \\ 
  4 
\end{array}} \right)\,\, + \,\,\left( {\begin{array}{*{20}{c}}
  {51} \\ 
  3 
\end{array}} \right)\, + \,\,\left( {\begin{array}{*{20}{c}}
  {52} \\ 
  3 
\end{array}} \right)\,\, + \,\,\left( {\begin{array}{*{20}{c}}
  {53} \\ 
  3 
\end{array}} \right)\,\, + \,\,\left( {\begin{array}{*{20}{c}}
  {54} \\ 
  3 
\end{array}} \right)\,\, + \,\,\,\left( {\begin{array}{*{20}{c}}
  {55} \\ 
  3 
\end{array}} \right)$

$ = \,\,\left( {\begin{array}{*{20}{c}}
  {52} \\ 
  4 
\end{array}} \right)\,\, + \,\,\left( {\begin{array}{*{20}{c}}
  {52} \\ 
  3 
\end{array}} \right)\,\, + \,\,\left( {\begin{array}{*{20}{c}}
  {53} \\ 
  3 
\end{array}} \right)\,\, + \,\,\left( {\begin{array}{*{20}{c}}
  {54} \\ 
  3 
\end{array}} \right)\,\, + \,\,\left( {\begin{array}{*{20}{c}}
  {55} \\ 
  3 
\end{array}} \right)\,\,$

$ = \,\,\,\left( {\begin{array}{*{20}{c}}
  {53} \\ 
  4 
\end{array}} \right)\,\, + \,\,\left( {\begin{array}{*{20}{c}}
  {53} \\ 
  3 
\end{array}} \right)\,\, + \,\,\left( {\begin{array}{*{20}{c}}
  {54} \\ 
  3 
\end{array}} \right)\,\, + \,\,\left( {\begin{array}{*{20}{c}}
  {55} \\ 
  3 
\end{array}} \right)$

$ = \left( {\begin{array}{*{20}{c}}
  {54} \\ 
  4 
\end{array}} \right)\,\, + \,\,\left( {\begin{array}{*{20}{c}}
  {54} \\ 
  3 
\end{array}} \right)\,\, + \,\,\left( {\begin{array}{*{20}{c}}
  {55} \\ 
  3 
\end{array}} \right)$

$ = \left( {\begin{array}{*{20}{c}}
  {55} \\ 
  4 
\end{array}} \right)\,\, + \,\left( {\begin{array}{*{20}{c}}
  {55} \\ 
  3 
\end{array}} \right)\,\,\,$

$ = \,\,\left( {\begin{array}{*{20}{c}}
  {56} \\ 
  4 
\end{array}} \right)$

Standard 11
Mathematics

Similar Questions

Start a Free Trial Now

Confusing about what to choose? Our team will schedule a demo shortly.