Counting Rectangles

Date: 05/23/2001 at 08:34:36
From: Michael Calabrese
Subject: Columns and rows

Find the Rule:

Discover the rule for finding the number of different rectangles in a 
square grid containing "c" columns and "r" rows.
get help from wherever we can.

Thanks,
Michael

Date: 05/23/2001 at 12:49:56
From: Doctor Peterson
Subject: Re: Columns and rows

Hi, Michael.

This is a fun problem, and I don't want to spoil it for you, so I'll 
just give you a hint. Think about how you can choose a rectangle. You 
can choose any pair of horizontal lines to make the top and bottom 
rows of your rectangle, and you can choose any pair of vertical lines 
to make the left and right columns. So to count all the rectangles you 
can make, you first have to decide how many ways you can choose the 
rows; then for each choice, you have the same number of ways to choose 
the columns, so you can multiply.

If you haven't learned about Permutations and Combinations, you may 
want to see the Dr. Math FAQ:

  http://mathforum.org/dr.math/faq/faq.comb.perm.html   

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/