The number of ways of dividing $52$ cards amongst four players so that three players have $17$ cards each and the fourth player just one card, is

Let $A_1,A_2,........A_{11}$ are players in a team with their T-shirts numbered $1,2,.....11$. Hundred gold coins were won by the team in the final match of the series. These coins is to be distributed among the players such that each player gets atleast one coin more than the number on his T-shirt but captain and vice captain get atleast $5$ and $3$ coins respectively more than the number on their respective T-shirts, then in how many different ways these coins can be distributed ?

The sum $\sum\limits_{i = 0}^m {\left( {\begin{array}{*{20}{c}}{10}\\i\end{array}} \right)} \,\left( {\begin{array}{*{20}{c}}{20}\\{m - i}\end{array}} \right)\,,$ $\left( {{\rm{where}}\,\left( {\begin{array}{*{20}{c}}p\\q\end{array}} \right)\, = 0\,{\rm{if}}\,p < q} \right)$, is maximum when m is

The number of ways of dividing $52$ cards amongst four players equally, are

Two packs of $52$ cards are shuffled together. The number of ways in which a man can be dealt $26$ cards so that he does not get two cards of the same suit and same denomination is

A student is to answer $10$ out of $13$ questions in an examination such that he must choose at least $4$ from the first five questions. The number of choices available to him is