In a class of 28 students, the teacher selects four people at random to participate in a geography contest. What is the probability that this group of four students includes at least one of the top three geography students in the class? Express your answer as a common fraction.
The probability = 1 minus the probability that none of the top three geography students are selected =
1 - (any group of 4 that does not include the top three students) / ( the total possible groups of four)
1 - C(25 , 4) / C (28 , 4) =
1 - 12650 / 20475 =
1 - 506 / 819 =
313 / 819