$A$ parallelogram is cut by two sets of $m$ lines parallel to its sides. The number of parallelograms thus formed is

Two lines $l_1$ and $l_2$ intersect at a point $P$. If $A_1, B_1, C_1$ are points on $l_1$ and $A_2, B_2, C_2, D_2, E_2$ are points on $l_2$,and none of these points coincide with $P$,how many triangles can be formed using these $8$ points?

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 -

In how many ways can $5$ boys and $5$ girls stand in a row so that no two girls may be together?

If $a, b, c, d$ are four distinct numbers chosen from the set $\{1, 2, 3, \ldots, 9\}$,then the minimum value of $\frac{a}{b} + \frac{c}{d}$ is

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: