Let's say you have a group of 22 people, which you would like to break into 5 different groups -- 3 groups of 4 and 2 groups of 5. How many distinct ways can you form such groups? I don't want to double count groups. Let's say I number the people from A - V. The group ABCDE and ACDBE should be considered the same group since they have the same elements. I imagine the numerator is [(22 choose 4)(18 choose 4)(14 choose 4)(10 choose 5)(5 choose 5) ] I'm not sure what to divide by to get rid of counting extras.