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

Let $P_{1}, P_{2}, \ldots, P_{15}$ be $15$ points on a circle. The number of distinct triangles formed by points $P_{i}, P_{j}, P_{k}$ such that $i+j+k \neq 15$ is:

Ten points lie in a plane such that no three of them are collinear. The number of lines passing through exactly two of these points and dividing the plane into two regions,each containing four of the remaining points,is

There are $n$ points in a plane,of which $p$ points are collinear. How many lines can be formed from these points?

The number of triangles whose vertices are the points $(x, y)$ in the $XY$-plane with integer coordinates satisfying $0 \leq x \leq 4$ and $0 \leq y \leq 4$ is:

In a plane,there are $37$ straight lines,of which $13$ pass through point $A$ and $11$ pass through point $B$. Moreover,no three lines (apart from the lines passing through $A$ and $B$) pass through the same point,and no two lines are parallel. What is the number of points of intersection of the straight lines?