There are 4 identical boxes, each containing 3 red balls and 2 blue balls. All 20 balls are distinguishable from one another. In how many ways can exactly 10 balls be selected from these 4 boxes such that from every box at least one red and at least one blue ball is chosen?

Question

Accepted Answer

21816. The only feasible distribution types are {4,2,2,2} (and its 4 permutations, giving 4 * 6³ * 5 = 4320) and {3,3,2,2} (and its 6 permutations, giving 6 * 9² * 6² = 17496); their sum is 21816.

There are 4 identical boxes, each containing 3 red balls and 2 blue balls. All 20 balls are distinguishable from one another. In how many ways can exactly 10 balls be selected from these 4 boxes such that from every box at least one red and at least one blue ball is chosen?

Solution

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