There are $16$ points in a plane out of which $6$ are collinear. How many lines can be drawn by joining these points?

There are $3$ girls in a class of $10$ students. The number of different ways in which they can be seated in a row such that no two of the three girls are together is

In a row,$6$ boys and $6$ girls are arranged at random. Find the probability that all $6$ girls are together.

Three of six vertices of a regular hexagon are chosen at random. The probability that the triangle formed by these three vertices is equilateral is

The sum of all absolute values of the differences of the numbers $1, 2, 3, \ldots, n$,taken two at a time,i.e.,$\sum \limits_{1 \leq j < i \leq n} |i-j|$ equals:

There are $m$ men and $2$ women participating in a chess tournament. Each participant plays $2$ games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by $84$,then the value of $m$ is