$n$ gentlemen can be made to sit on a round table in how many ways?

The value of $^{15}C_3 + ^{15}C_{13}$ is

$A$ teacher of a class wants to set $1$ question from each of $2$ exercises in a book. If there are $15$ and $12$ questions in the $2$ exercises respectively,then in how many ways can the $2$ questions be selected?

Six '$X$'s have to be placed in the squares of the figure such that each row contains at least one '$X$'. In how many different ways can this be done?

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:

$A$ man has $10$ friends. In how many ways can he invite one or more of them to a party?