Ten distinct points are identified on the circumference of a circle. How many different convex quadrilaterals can be formed if each vertex must be one of these 10 points?
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+770 finition A polygon is said to be convex if it fully contains all line segments drawn between any two points of the polygon. Once four vertices have been selected, the quadrilateral is determined, regardless of the order of the vertices. So this is just a combination problem. We seek the number of combinations of 10 things taken 4 at a time: C(10, 4) = 10C4 = 10! 4! / (10 − 4)! = 10 × 9 × 8 × 7 / 4 × 3 × 2 × 1 = 210
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