Counting rectangles on an 8 by 8 board

Question

Counting squares as rectangles too, how many rectangles made up of whole cells can be found on an $8\times8$ chessboard?

Short answer

$1296$ . A rectangle is fixed by choosing two of the $9$ vertical grid lines and two of the $9$ horizontal grid lines, so the count is $\binom92^2=36^2$ .

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Lessons behind this question

Counting and Combinatorics
Sample Spaces, Events, and the Probability Axioms
Conditional Probability, Total Probability, and Bayes' Rule

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