Out of $10$ points in a plane,$6$ are collinear. How many triangles can be formed by joining these points?

Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently equals

In a plane,there are $37$ straight lines,of which $13$ pass through the point $A$ and $11$ pass through the point $B$. Besides,no three lines pass through one point,no line passes through both points $A$ and $B$,and no two lines are parallel. The number of intersection points the lines have is equal to:

Ten points are marked on a circle. The number of distinct convex polygons of three or more sides that can be drawn using some or all of the ten points as vertices is:

There are $12$ points in a plane,no three of which are in the same straight line,except $5$ points which are collinear. Then the total number of triangles that can be formed with the vertices at any three of these $12$ points is

The number of diagonals in a polygon of $m$ sides is