The total number of possible ways in which a person can go from $A(0,0)$ to $B(3,3)$ if he can travel only to the right or upward along the grid lines is:

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:

Let $S = \{(a, b) : a, b \in \mathbb{Z}, 0 \leq a, b \leq 18\}$. The number of lines in $\mathbb{R}^2$ passing through $(0,0)$ and exactly one other point in $S$ is:

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

There are $n$ distinct points on a circle. If the number of pentagons that can be formed using these points as vertices is equal to the number of triangles that can be formed,then the value of $n$ is:

There are $10$ points in a plane,out of which $6$ are collinear. If $N$ is the number of triangles formed by joining these points,then . . . .