The greatest positive integer which divides $(n+16)(n+17)(n+18)(n+19)$,for all positive integers $n$,is

The number of ways in which $21$ identical apples can be distributed among three children such that each child gets at least $2$ apples,is

There are ten boys $B_{1}, B_{2}, \ldots, B_{10}$ and five girls $G_{1}, G_{2}, \ldots, G_{5}$ in a class. The number of ways of forming a group consisting of three boys and three girls,such that $B_{1}$ and $B_{2}$ are not both members of the same group,is

If a committee of $10$ members is to be formed from $8$ men and $6$ women,then the number of different possible committees in which the men are in majority is

Mahesh has $6$ friends. In how many ways can he invite one or more friends for dinner?

If the total number of $m$-element subsets of the set $A = \{a_{1}, a_{2}, \ldots, a_{n}\}$ is $k$ times the number of $m$-element subsets containing $a_{4}$, then $n$ is