Problem
COM-B1-M04-P019 Rectangles by Pairs of Lines
#19
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How many rectangles are in a \(5\) by \(6\) grid of cells?
Choose two vertical and two horizontal grid lines.
A \(5\) by \(6\) grid has \(6\) horizontal and \(7\) vertical lines. A rectangle is determined by choosing two vertical and two horizontal lines. Answer: \(C(7,2)C(6,2)=21\cdot15=315\).
Counting rectangle boundaries.