If a set of 10 parallel lines are intersected by a set of 13 other parallel lines,then find the number of parallelograms formed?
I m not able to undertsand the question ..is there a standard formula for this type of questions
Let $\displaystyle S_1, \ S_2$ be the two sets of parallel lines. A paralleogram is formed by a pair of lines from $\displaystyle S_1$ and a pair of lines from $\displaystyle S_2$. So, the number of parallelograms depends on how many pairs can take from $\displaystyle S_1$ and $\displaystyle S_2$.
This number is $\displaystyle C_{10}^2\cdot C_{13}^2=45\cdot 78=3510$
Generally, if there is a set of n parallel lines and another set of m parallel lines, the number of parallelograms is $\displaystyle C_n^2\cdot C_m^2$
will this formula hold good if both m and n are equal like in a chess board 9 parallel lines intersecting 9 parallel lines so if i apply ur formula 9C2*9C2 is not equal to 64 .
so i did like this number of lines -1C (min number of lines -1)
so 22-1C10-1=21C9