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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.

Lightning  Apr 27, 2018
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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.

I think the number of ways that choice can be made is ...

$$\binom{3}{2}*\binom{25}{2}+\binom{3}{3}*\binom{25}{1}\\ =3*300+1*25\\ =900+25\\ =925$$

And the total number of possibilities is  28C4 = 20475

So the prob is    $$\frac{925}{20475} = \frac{37}{819}$$

Melody  Apr 27, 2018

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