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Bunuel

The circle above has 10 points on its edge. How many different hexagons can be drawn that use six of these points as its vertices?

A. 30,240
B. 1,008
C. 252
D. 210
E. 10

Since the circle has 10 points on its edge and we need to create hexagons, each of which has 6 vertices, the number of ways to create those quadrilaterals using the 10 points is 10C6:

10!/[6!(10 - 6)!] = 10!/(6! x 4!) = (10 x 9 x 8 x 7)/4! = (10 x 9 x 8 x 7)/(4 x 3 x 2) = 10 x 3 x 7 = 210

Answer: D
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