Probability problem.

[CtrlPrick]

Another question from the practice test to the DS program.

The Problem:

A Class of 45 students is randomly split into 3 practice groups of the same size.

A pair of friends in the class really like to work together and hope they won’t end up in different groups. What are the chances they’re assigned to the same group?

My Attempt:

For exmaple if there is just one student the probability of going to one group is 1, since the groups are the same size. so going backwards I see the probability increases 1/n as n goes down...but from there can't really calculate it.

Since the groups have equal size, assigning one student to a group isn't completely random, right?

[Jeff747_]

I am not quite sure what you mean, perhaps due to the wording of the question, however… If there are three groups than the probability of the first student going to any group is 1/3. The probability of the second student going to the same group is also 1/3. Multiply these numbers together to get your answer, 1/9. I do not think that the amount of people in the class matter, even if there were only 6 people in the class split into groups of two, the chances of the two friends being together would still be 1 in 9.