How to find the number of non degenerate triangles in the Cartesian plane whose vertices lie in the set$ \{(x, y) : 0\le x\le7 , 0\le y\le7\}$ . I don't have any idea how to solve it...
2026-04-18 22:25:55.1776551155
Number of triangles.
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You have $64$ points in your set, so ignoring the degenerate condition there are $64\choose 3$ triangles. For a triangle to be degenerate, the three points need to be on the same line, so find all the lines that have three or more points on them and subtract the number of ways to select three from one of them.