$A$ polygon has $54$ diagonals. The number of sides of this polygon is

Five boys and three girls are seated in a row at random. What is the probability that all three girls sit together?

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

$l_1, l_2, l_3$ are three parallel lines in the same plane. If there are $m$ points on $l_1$,$n$ points on $l_2$,and $k$ points on $l_3$,what is the maximum number of triangles that can be formed with vertices at these points?

Six boys and six girls sit in a row randomly. What is the probability that the six girls sit together?

$p$ points are chosen on each of the three coplanar lines. The maximum number of triangles formed with vertices at these points is