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A quadrilateral is formed from 4 points where at most 2 can be colinear.

So, from total subtract unwanted possibilities

(Total ways) - (ways to pick 4 colinear points) - (ways to pick 3 colinear points)

ans = ^{25}C_{4} - ^{7}C_{4} - ^{7}C_{3} . ^{18}C_{1}