Seven points are randomly placed on the circle shown below.
How many different triangles can be drawn using these points as vertices?
Solution
There are 35 possible triangles. If we label the points A, B, C, D, E, F, and G then the triangles are: ABC, ABD, ABE, ABF, ABG, ACD, ACE, ACF, ACG, ADE, ADF, ADG, AEF, AEG, AFG, BCD, BCE, BCF, BCG, BDE, BDF, BDG, BEF, BEG, BFG, CDE, CDF, CDG, CEF, CEG, CFG, DEF, DEG, DFG, and EFG.
How many quadrilaterals are possible? Would there be more quadrilaterals or more triangles? Is there a quick way to figure out how many quadrilaterals there would be?
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