Class divided into 5, probability of 2 people in the same team This might be a very simple question, but: a class of 25 students is divided into 5 teams of 5 each. What is the probability of student X and Y being in the same team?
is it just 4/25?

Imagine that our heroes, A and B, are assigned to teams, in that order, with the rest being assigned later.
Whatever team A is assigned to, there are $4$ empty spots on that team. The probability B is given one of these spots is $\frac{4}{24}$. 
Or else we can do more elaborate counting. Imagine the teams are labelled (it makes no difference to the probability). There are 
$\binom{25}{5}\binom{20}{5}\binom{15}{5}\binom{10}{5}\binom{5}{5}$ ways to assign the people to labelled teams, all equally likely.
Now we count the number of ways A and B can end up on the same team. Which team? It can be chosen in $5$ ways. The other $3$ people on that team can be chosen in $\binom{23}{3}$ ways. And the rest of the assignments can be done in $\binom{20}{5}\binom{15}{5}\binom{10}{5}\binom{5}{5}$ ways. 
Divide. We get that the probability is $\frac{5\binom{23}{3}}{\binom{25}{5}}$. This simplifies to $\frac{1}{6}$. 
