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Question

Answer 1

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׳C₃=4

So Net total = 560-40-4 = 516

Comments

now, corrected; it is 4x4 dots, i was wrong

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you said 10 lines but multiplied with 8.why??you should multiply by 10 right??

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now, check it