In a plane,there are $10$ points,out of which $4$ are collinear. The number of triangles that can be formed by joining these points is:

On the sides $AB, BC, CA$ of a $\Delta ABC$,$3, 4, 5$ distinct points (excluding vertices $A, B, C$) are respectively chosen. The number of triangles that can be constructed using these chosen points as vertices is:

The number of rectangles that can be obtained by joining four of $12$ vertices of a $12$-sided regular polygon is:

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

Ten points lie in a plane such that no three of them are collinear. The number of lines passing through exactly two of these points and dividing the plane into two regions,each containing four of the remaining points,is

In how many ways can $5$ boys and $3$ girls sit in a row so that no two girls are together?