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There are 6 equally spaced points A, B, C, D, E and F marked on a circle with radius R. How many convex heptagons of distinctly different areas can be drawn using these points as vertices?

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There are 6 equally spaced points A, B, C, D, E and F marked on a circle with radius R. How many convex heptagons of distinctly different areas can be drawn using these points as vertices?

(a) 7! * 6

(b) 7C5

(c) 7!

(d) same area

This question was addressed to me in unit test.

The doubt is from Counting in portion Counting of Discrete Mathematics

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Right choice is (d) same area

The best I can explain: Since all the points are equally spaced; hence the area of all the convex heptagons will be the same.

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