In how many different ways can we arrange 120 students into 6 groups for 6 different classes so that the largest group has at most 2 members more than the smallest group?
My initial plan was to use a generating function, but I stumbled across a problem. Let's mark the groups with numbers 1 to 6 and let denote the number of members of the i-th group in some arrangment. To see where this would lead me, for a moment, I assumed in hope to find some range for 's and use a generating function and find the coefficient in front of , however students are distinct entities and m and M still remained misterious. I then tried figuring out if I was on the somewhat right track by, again taking and write . I believe, an arrangement with 2 groups of 19,2 groups of 20 and 2 groups of 21 people suggests there should be at least 19 people in each group.