How many necklaces can be formed by selecting $4$ beads from $6$ different colored glass beads and $4$ beads from $5$ different colored metal beads?

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:

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

If four points are taken on each of three parallel lines in a plane,then the maximum number of triangles formed with these points is

The lines $L_1, L_2, \ldots, L_{20}$ are distinct. For $n=1, 2, 3, \ldots, 10$,all the lines $L_{2n-1}$ are parallel to each other,and all the lines $L_{2n}$ pass through a given point $P$. The maximum number of points of intersection of pairs of lines from the set $\{L_1, L_2, \ldots, L_{20}\}$ is equal to:

If the number of diagonals of a regular polygon is $35$,then the number of sides of the polygon is