There are 9 students in Ms. Q's class. Ms. Q wants to split up her class into three groups for a group project, and wants each group to have at least two students. In how many ways can she do this?
There are three cases to consider:
Case 1: Each group has 2 students. Then there are (29)=36 ways to form the groups.
Case 2: One of the groups has 3 students and the other two groups have 2 students each. Then there are (39)=84 ways to choose which student is in the group of 3, and then 3 ways to order the 3 students in that group.
Case 3: One of the groups has 4 students and the other two groups have 1 student each. Then there are (49)=126 ways to choose which student is in the group of 4, and then 4 ways to order the 4 students in that group.
Summing the number of ways in each case, we get a total of 36+84+126=246 ways to form the groups.
