$110$ triangles can be formed by joining $10$ points as vertices,in which $n$ points are collinear. Then the value of $n$ is:

There are $10$ points in a plane of which no three points are collinear except $4$ points. The number of distinct triangles that can be formed by joining these points such that at least one of the vertices of every triangle formed is from the given $4$ collinear 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:

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

Four distinct numbers are randomly selected out of the set of first $20$ natural numbers. The probability that no two of them are consecutive 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: