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

$A$ test consists of $6$ multiple choice questions,each having $4$ alternative answers of which only one is correct. The number of ways in which a candidate answers all six questions such that exactly four of the answers are correct is:

The number of permutations of $n$ things taken $r$ at a time,when $p$ things are always included,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?

In how many ways can $5$ sportsmen be selected from a group of $10$?

In how many ways can a committee,consisting of $5$ men and $6$ women,be formed from $8$ men and $10$ women?