I have come across this problem and I can't quite figure out the solution.
A class of 60 students is divided into 3 groups of 20 randomly. Three friends are in this year group. Find the probability that all three of them are in different classes.
The answer given is 800/3422
However I work out that: A) The probability that all of them are in the same class is: 20/60x19/59/18/58x3x3 where the first three is for all the classes and the second three is to account for the 3 different students. This is 1026/3422
B) I find the probability that 2 are on the same class and one is on a different class. 20/60x19/59x40/58x6. 6 is for all the possible combinations of classes. I get 1520/3422
C) Last step is that all the cases should add up to 1 so I get that the probability that the students are in different classes is 876/3422.
I obviously have made a mistake. Can anyone spot it? Thank you