SOLUTION: In how many ways can 12 children be placed on 3 different teams of 3, 5, and 4 members?

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Question 703314: In how many ways can 12 children be placed on 3 different teams of 3, 5, and 4 members?
Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
C(12,3)×C(9,5)×C(4,4) = 220×126×1 = 27720

Notice that it won't matter what order you place them on the teams,
because you get the same answer, regardless:

C(12,3)×C(9,4)×C(5,5) = 220×126×1 = 27720

C(12,5)×C(7,3)×C(4,4) = 792×35×1 = 27720

C(12,5)×C(7,4)×C(3,3) = 792×35×1 = 27720

C(12,4)×C(8,3)×C(5,5) = 495×56×1 = 27720

C(12,4)×C(8,5)×C(3,3) = 495×56×1 = 27720

Edwin