Math Problem Statement
The following figure consists of 7 horizontal lines and 13 vertical lines. The goal is to count the number of rectangles (including squares, as they are a subset of rectangles) that can be formed. Define a function f: R → V × H, where R is the set of all rectangles, V is the set of all sets of two vertical lines, and H is the set of all sets of two horizontal lines.
Solution
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image_path = "/mnt/data/17336376030794vjjz0qf.jpg" img = Image.open(image_path)
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Math Problem Analysis
Mathematical Concepts
Combinatorics
Geometry
Formulas
Combination formula: C(n, k) = n! / (k!(n-k)!)
Counting rectangles: Total = C(vertical_lines, 2) × C(horizontal_lines, 2)
Theorems
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Suitable Grade Level
Grades 10-12