Three parallel straight lines $L_1, L_2$ and $L_3$ lie on the same plane. Consider $5$ points on $L_1, 7$ points on $L_2$ and $9$ points on $L_3$. Then the maximum possible number of triangles formed with vertices at these points is:

If $p$ points are taken on each of the three coplanar parallel lines,what is the maximum number of triangles that can be formed with vertices at these points?

There were two women participating in a chess tournament. Every participant played two games with every other participant. The number of games that the men played between themselves exceeded the number of games that the men played with the women by $66$. The total number of participants is

Out of $30$ points in a plane,$8$ of them are collinear. The number of straight lines that can be formed by joining these points is:

Out of $10$ points in a plane,$6$ are in a straight line. The number of triangles formed by joining these points is:

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