Suppose Anil's mother wants to give $5$ whole fruits to Anil from a basket of $7$ red apples, $5$ white apples and $8$ oranges. If in the selected $5$ fruits, at least $2$ orange, at least one red apple and at least one white apple must be given, then the number of ways, Anil's mother can offer $5$ fruits to Anil is $........$

All possible two factors products are formed from numbers $1, 2, 3, 4, ...., 200$. The number of factors out of the total obtained which are multiples of $5$ is

The least value of natural number $n$ satisfying $C(n,\,5) + C(n,\,6)\,\, > C(n + 1,\,5)$ is

The number of ways in which thirty five apples can be distributed among $3$ boys so that each can have any number of apples, is

The number of ways in which any four letters can be selected from the word ‘$CORGOO$’ 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