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## Main Question or Discussion Point

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.

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.