There are $15$ buses running between Delhi and Mumbai. In how many ways can a man go to Mumbai and return by a different bus?

There are $15$ persons in a party and each person shakes hands with every other person exactly once. What is the total number of handshakes?

Four dice (six-faced) are rolled. The number of possible outcomes in which at least one die shows $2$ is

How many $3$-digit numbers can be formed by using the digits $0, 2, 3, 6, 8$ when the digits may be repeated any number of times?

The number of integers greater than a million that can be formed using the digits $2, 3, 0, 3, 4, 2, 3$ is:

Consider three boxes,each containing $10$ balls labelled $1, 2, dots, 10$. Suppose one ball is randomly drawn from each of the boxes. Denote by $n_i$ the label of the ball drawn from the $i^{th}$ box,$(i = 1, 2, 3)$. Then,the number of ways in which the balls can be chosen such that $n_1 < n_2 < n_3$ is: