# Parallelograms formed by parallel lines

Given in figure 4, there are 5 parallel lines intersected by 4 other parallel lines. How many unique parallelograms are there in figure 4?

Answer: 60. When two pairs of parallel lines intersect, one parallelogram forms -> number of parallelograms are

vector(4, 2) * vector(5, 2) = 6 * 10 = 60

I'm confused on how the 6 and 10 appeared. I thought dot notation would dictate that the answer be 24? Unless, I am completely mistaken and the two were not written as vectors. Any help would be greatly appreciated!

$${4\choose2}\cdot{5\choose2}=6\cdot10$$
Those aren't vectors, but rather binomial coefficents, pronounced "($4$ choose $2$) times ($5$ choose $2$)".
$${n\choose k}=\frac{n!}{k!(n-k)!}$$