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Total ways of selecting 3 vertices: 16C3 = 560

but it included the linear vertices. (3 vertices in same line)

total 10 lines (4 vertical + 4 horizontal + 2 digonal ) which contains 4 elements

so remove these = 10 lines × one line contains (4C3) = 40

and there are 4 cross lines (up and down to digonal) which contain exact 3 vertices = 4×3C3=4

So Net total = 560-40-4 = 516

edited by

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