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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 two of the top three geography students in the class? Express your answer as a common fraction.

 Nov 4, 2019
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Total number of  possible sets  =  C(28,4)  =  20, 475

 

Total number of sets  that include 2 of the top 3 students  = C(3,2) * C(25, 2)  = 3*300  = 900

Total number of sets that include all three top students  = C(3,3) * C(25, 1) =  1 * 25 =  25

 

So....the probability that we choose at least 2 of the top 3 students  = 

 

[900 + 25 ]  / 20,475  =   925/ 20475  =    37 / 819

 

 

cool cool cool

 Nov 4, 2019
edited by CPhill  Nov 4, 2019

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