In how many ways can $5$ prizes be distributed among four students when every student can take one or more prizes?

Choose the correct number of ways in which $15$ different books can be divided into five heaps of equal number of books.

Let the eleven letters $A, B, \dots, K$ denote an arbitrary permutation of the integers $(1, 2, \dots, 11)$. Then, the product $(A - 1)(B - 2)(C - 3) \dots (K - 11)$ is:

The number of ways in which first,second and third prizes can be given to $5$ competitors is

The number of integers between $1$ and $10^{10}$ (inclusive) that contain the digit $1$ is:

There are $6$ men and $8$ women in a club in which a committee of $5$ people has to be formed. What will be the number of ways to select $5$ people if no man is selected?