Final answer:
The number of rectangles that can be formed from an m by n board is calculated by selecting two distinct horizontal and vertical lines to form a rectangle. The total number of rectangles is the product of m choose 2 and n choose 2, yielding (m(m-1)/2) * (n(n-1)/2).
Step-by-step explanation:
The question on how many rectangles can be formed from an m by n board is related to a combinatorial problem in mathematics. To calculate the number of rectangles, we can select two distinct vertical lines and two distinct horizontal lines to form a rectangle. On an m by n board, there are m horizontal lines and n vertical lines.
We have m choose 2 ways to choose two horizontal lines and n choose 2 ways to choose two vertical lines. The total number of rectangles is therefore the product of these two choices, which is given by:
The number of rectangles = (m choose 2) * (n choose 2) = (m(m-1)/2) * (n(n-1)/2).