ABCD is a square. One point on each of AB and CD; and two distinct points on each of BC and DA are chosen. How many distinct triangles can be drawn using any three points as vertices out of these six points?

Question

Aicharya · Accepted Answer

There are 6 points: 1 on AB, 1 on CD, 2 on BC, 2 on DA. Total ways to choose 3 points $= \binom{6}{3} = 20$. No set of three of these six points is collinear (each side has at most 2 chosen points). Total distinct triangles $= 20$.

ABCD is a square. One point on each of AB and CD; and two distinct points on each of BC and DA are chosen.…

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