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Diagonals of a pentagon

Source: 2012-2013 SDML Middle School 1a Problem 10

August 24, 2016

Problem Statement

Two of the diagonals of a regular pentagon are selected at random. What is the probability that the two selected diagonals intersect inside the pentagon?
(A) 25(B) 15(C) 710(D) 35(E) 12\text{(A) }\frac{2}{5}\qquad\text{(B) }\frac{1}{5}\qquad\text{(C) }\frac{7}{10}\qquad\text{(D) }\frac{3}{5}\qquad\text{(E) }\frac{1}{2}
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