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Colored shirts at work

Source: 2014-2015 SDML Middle School 1a Problem 4

August 28, 2016

Problem Statement

Shannon, Laura, and Tasha found a shirt which came in five colors at their favorite store, and they each bought one of each color of that shirt. On Monday, they all wear one of their new shirts to work. What is the probability that Shannon, Laura, and Tasha will not all be wearing the same color shirt that day?
(A) 1225(B) 1625(C) 2125(D) 2225(E) 2425\text{(A) }\frac{12}{25}\qquad\text{(B) }\frac{16}{25}\qquad\text{(C) }\frac{21}{25}\qquad\text{(D) }\frac{22}{25}\qquad\text{(E) }\frac{24}{25}