This was a question on a recent test and I was hoping for a conclusive answer and reasoning behind it.
A local university housing office has a problem. It has 11 students to squeeze into 3 dorm rooms. It has been decided that 3 students are to be assigned to the first room, 6 students are to be assigned to the second room and 2 students are to be assigned to the third room. In how many ways can this assignment of 11 students be accomplished?
[Edit: As I recall,] the answer provided was: $11 \choose 3$ + $8 \choose 6$ + $2 \choose 2$ = 194
What I don't understand is why order matters in choosing how many students are assigned to each dorm. That is, why should the answer be different if 6 students are chosen for the first room and 3 chosen for the second?