From $6$ different novels and $3$ different dictionaries, $4$ novels and $1$ dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is :

The number of ways in which $21$ identical apples can be distributed among three children such that each child gets at least $2$ apples, is

A committee of $7$ has to be formed from $9$ boys and $4$ girls. In how many ways can this be done when the committee consists of: 

exactly $3$ girls $?$

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

If $^{10}{C_r}{ = ^{10}}{C_{r + 2}}$, then $^5{C_r}$ equals

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 question. The number of choices available to him is