How many triangles can be formed by joining four points on a circle?

Find the total number of rectangles on a normal chessboard.

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.

The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the octagon is

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

The number of ways in which $3$ boys and $2$ girls can sit on a bench so that no two boys are adjacent is . . . . . .