In how many ways can $5$ red and $4$ white balls be drawn from a bag containing $10$ red and $8$ white balls?

$A$ committee of $5$ members is to be formed out of $3$ trainees,$4$ professors,and $6$ research associates. In how many different ways can this be done if the committee must have $2$ trainees and $3$ research associates?

In how many ways can $3$ letters be posted in $4$ letter-boxes,if all the letters are not posted in the same letter-box?

If $n$ and $r$ are two positive integers such that $n \ge r,$ then $^nC_{r-1} + ^nC_r = $

$6$ points in a plane are joined in all possible ways by indefinite straight lines. If no two lines are coincident or parallel,and no three lines pass through the same point (with the exception of the original $6$ points),the number of distinct points of intersection is equal to

How many $4$-digit numbers are there with distinct digits?