Number of positive integral solution of the equation $xyz = 90$ is equal to :-

In a touring cricket team there are $16$ players in all including $5$ bowlers and $2$ wicket-keepers. How many teams of $11$ players from these, can be chosen, so as to include three bowlers and one wicket-keeper

The number of ways in which $3$ children can distribute $10$ tickets out of $15$ consecutively numbered tickets themselves such that they get consecutive blocks of $5, 3 $ and $2$ tickets is

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

There are three bags $B_1$,$B_2$ and $B_3$ containing $2$ Red and $3$ White, $5$ Red and $5$ White, $3$ Red and $2$ White balls respectively. A ball is drawn from bag $B_1$ and placed in bag $B_2$, then a ball is drawn from bag $B_2$ and placed in bag $B_3$, then a ball is drawn from bag $B_3$. The number of ways in which this process can be completed, if same colour balls are used in first and second transfers (Assume all balls to be different) is

If $^n{C_{r - 1}} = 36,{\;^n}{C_r} = 84$ and $^n{C_{r + 1}} = 126$, then the value of $r$ is