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

#1**+1 **

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