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?

In a conference of $8$ persons,if each person shakes hands with every other person exactly once,then the total number of handshakes is:

$P_1$ and $P_2$ are two distinct and intersecting planes. Three non-collinear points lie on $P_1$ and another three non-collinear points lie on $P_2$ (none being on the line of intersection of the planes). Then,the maximum number of tetrahedrons formed using these six points is:

The number of numbers between $2,000$ and $5,000$ that can be formed using the digits $0, 1, 2, 3, 4$ (repetition of digits is not allowed) which are multiples of $3$ is?

The number of ways in which one or more balls can be selected out of $10$ white,$9$ green,and $7$ blue balls are:

$^{n - 1}C_r = (k^2 - 3) \cdot ^nC_{r + 1}$ if $k \in$