There are $8$ points in a plane,out of which $4$ are collinear. How many triangles can be formed by joining these points?

$m$ men and $n$ women are to be seated in a row so that no two women sit together. If $m > n$,then the number of ways in which they can be seated is

If a polygon has $44$ diagonals,then the number of its sides is:

Five boys and three girls are seated in a row at random. What is the probability that all three girls sit together?

Let $ABC$ be a triangle. Consider four points $p_1, p_2, p_3, p_4$ on the side $AB$, five points $p_5, p_6, p_7, p_8, p_9$ on the side $BC$, and four points $p_{10}, p_{11}, p_{12}, p_{13}$ on the side $AC$. None of these points is a vertex of the triangle $ABC$. The total number of pentagons that can be formed by taking all the vertices from the points $p_1, p_2, \ldots, p_{13}$ is . . . . . . .

There are two women participating with some men in a chess tournament. Each participant played two games with every other participant. The number of games that the men played between themselves is $66$ more than the number of games that the men played with the women. Find the total number of participants in the tournament.