There are $4$ men and $5$ women in Group $A$,and $5$ men and $4$ women in Group $B$. If $4$ persons are selected from each group,then the number of ways of selecting $4$ men and $4$ women is:

All possible words (with or without meaning) are formed by taking at least $2$ letters (all different) from the letters of the word '$CURVE$'. If a word is chosen at random from all the words thus formed,then the probability of getting a $3$-letter word is

The students $S_{1}, S_{2}, \ldots, S_{10}$ are to be divided into $3$ groups $A, B$ and $C$ such that each group has at least one student and the group $C$ has at most $3$ students. Then the total number of possibilities of forming such groups is ........ .

The sum of all $4$-digit numbers that can be formed using the digits $2, 3, 4, 5, 6$ without repetition is:

The difference between an integer $n$ and its cube $n^3$ is always divisible by which of the following?

Five balls of different colors are to be placed in three boxes of different sizes,where each box can hold all five balls. In how many ways can the balls be placed such that no box remains empty?