If ${ }^{n+4} C_{n+1}-{ }^{n+3} C_n=15(n+2)$, then $n=$

The greatest possible number of points of intersection of 8 distinct straight lines and 4 distinct circles is

4 red balls and 5 green balls are selected from $n$ balls. If the sum of both the selections is greater than ${ }^{n+1} C_4$ then the value of $n$ is equal to

A regular polygon has 20 sides. The number of triangles that can be drawn by using the vertices but not using the sides are