( * 20 c 50 4 ) , , + , , _ i = 1 ^6 ( * 20 c 56 , - ,i 3 ) = ...…

MCQ

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

A
$\left( {\begin{array}{*{20}{c}}{55}\\4\end{array}} \right)$
B
$\left( {\begin{array}{*{20}{c}}{55}\\3\end{array}} \right)$
C
$\left( {\begin{array}{*{20}{c}}{56}\\3\end{array}} \right)$
✓
$\left( {\begin{array}{*{20}{c}}{56}\\4\end{array}} \right)$

✓

Answer

Correct option: D.

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

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

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

$ = \,\,\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)$

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