# parallel lines

• Aug 18th 2009, 11:09 PM
arunachalam.s
parallel lines
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
• Aug 18th 2009, 11:52 PM
red_dog
Let $S_1, \ S_2$ be the two sets of parallel lines. A paralleogram is formed by a pair of lines from $S_1$ and a pair of lines from $S_2$. So, the number of parallelograms depends on how many pairs can take from $S_1$ and $S_2$.

This number is $C_{10}^2\cdot C_{13}^2=45\cdot 78=3510$

Generally, if there is a set of n parallel lines and another set of m parallel lines, the number of parallelograms is $C_n^2\cdot C_m^2$
• Aug 19th 2009, 01:08 AM
arunachalam.s
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
• Aug 19th 2009, 03:19 AM
Plato
Quote:

Originally Posted by arunachalam.s
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 .

You have a missunderstaning about the count.
Look at the attached 3x3 grid.
There are a total of nine rectangles in that grid: $\binom{3}{2}\binom{3}{2}=9$.
• Aug 19th 2009, 04:32 AM
arunachalam.s
k i understand thank u