$A$ student is to answer $10$ out of $13$ questions in an examination such that he must choose at least $4$ from the first $5$ questions. The number of choices available to him is

There are $6$ Men and $8$ Women in a club in which a committee of $5$ people has to be made. What will be the number of ways to select $5$ people if at most one man is selected?

If $^{2017}C_0 + ^{2017}C_1 + ^{2017}C_2 + ...... + ^{2017}C_{1008} = \lambda^2$ where $\lambda > 0$,then the remainder when $\lambda$ is divided by $33$ is:

In how many ways can $15$ different books be divided equally among $5$ sets or groups?

In an examination hall,there are $4$ rows of chairs. Each row has $8$ chairs,$1$ behind the other. There are $2$ classes sitting for the examination with $16$ students in each class. It is desired that in each row,all students belong to the same class and that no $2$ adjacent rows are allotted to the same class. In how many ways can these $32$ students be seated?

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?