## anonymous one year ago The following figure consists of 8 horizontal lines and 12 vertical lines. The goal of this problem is to count the number of rectangles (squares are a kind of rectangle, but line segments are not). WebAssign Plot Let V be the set of all sets of two vertical lines, and let H be the set of all sets of two horizontal lines. Let R be the set of all rectangles in the figure. Define a function f : R → V × H by f transform arrow ({AB, CD}, {AC, BD}). Compute |R|, the number of rectangles in the figure.

1. dan815

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2. dan815

okay i think i see what u have to do now, we have to go up the rows and the columns all separetely

3. dan815

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4. dan815

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5. dan815

i wrote it out, im thinking this should be written in a double summation, and then we can look for the clsoed form http://prntscr.com/7dphg2

6. ganeshie8

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7. dan815

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8. dan815

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9. dan815
10. dan815

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11. dan815

:O how is this formula in there

12. dan815

omg xD if we pick any 2 vertical lines and any 2 horizontal lines, we can have a unique intersection dang

13. dan815

whyyyyy didnnntt ii think of that sooner T_T

14. ganeshie8

that looks much simpler! nc2 ways to choose 2 vertical lines from n lines mc2 ways to choose 2 horizontal lines from m lines

15. dan815

yeah xD well this is a neat find either way lol

16. dan815

strange way to state it but ya

17. dan815

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