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How many ways are there to put 4 balls in 3 boxes if the balls are not distinguishable but the boxes are?

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Answer:

15 outcomes

Explanation:

the balls are all the same so the only differenciating thing is how many balls are in each individual box.

The boxes can have

0,0,4 3 possibilities

0,1,3 6 possibilities

0,2,2 3 possibilities

1,1,2 3 possibilities

So that are 15 unique outcomes

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