Separating 18 people into 5 teams A teacher wants to divide her class of 18 students into 5 teams to work on projects, 
with two teams of 3 students each and three teams of 4 students each.
a) In how many ways can she do this, if the teams are not numbered?
b) What is the probability that two of the students, Mia and Max, will be on the same team?
[This is not a homework problem.]

Starting with the "binomial(18, 3)+binomial(15, 3)+binomial(12, 4)+binomial(8, 4)+binomial(4, 4)" solution I got 1837 possible combinations, but if you start with dividing into the 4 teammember teams first I get "binomial(18, 4)+binomial(14, 4)+binomial(10, 4)+binomial(6, 3)+binomial(3, 3) = 4292 possible combinations", no idea if it's right or not just something to double check.
