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2018 AMC 8 Problems/Problem 23

From a regular octagon, a triangle is formed by connecting three randomly chosen vertices of the octagon. What is the probability that at least one of the sides of the triangle is also a side of the octagon?

 Jun 28, 2019

We can choose a triangle 8C3 ways or 8!/3!*5!=8*7=56 ways. If the three points are adjacent, then we have eight ways to place the points. and if we have two adjacent points, we have eight*four-=thrity-two possible cases. Thus, the answer is 8+32/56=40/56=5/7.

 Jun 29, 2019

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