Premutations and combinations 2

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To determine the number of rectangles that can be formed on a 5x4 grid, one must select 4 lines from the grid, specifically 2 horizontal and 2 vertical lines. There are 6 horizontal lines and 5 vertical lines available. The valid combinations include choosing 2 horizontal lines from the 6 and 2 vertical lines from the 5. The calculations involve using combinations to find the total number of unique rectangles that can be formed. Ultimately, the solution requires understanding the selection of lines that define the rectangle's corners.
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Four lattices are selected from 5*4 grid board indicated in the figure above so that they form the corners of a rectangle having sides parallel to the edges of the board. How many different rectangles can be formed in this way?
Can anyone give me some clues to answer this question?
Thanks:approve:
 

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You need to choose 4 lines from you lattice to make the rectangle. These 4 lines will decide what the 4 sides in your rectangle are.

What are the valid ways in which you can choose them?

Let's say there are 6 horizontal(H) and 5 vertical lines(V) in the grid.
Can you choose all four lines from only the horizontal set of lines? Similarly, can you choose all four lines from only the vertical set of lines?
How about 3H - 1V or 2H - 2V?
 
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Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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