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Six identical marbles are put into 3 identical boxes, and boxes may be empty. In how many ways can this be done?

Competition practicePermutations & Combinations
  • A28
  • B10
  • C7
  • D6

Step-by-Step Solution

Only the multiset of box sizes matters: 6+0+0, 5+1+0, 4+2+0, 4+1+1, 3+3+0, 3+2+1, 2+2+2. That is 7 ways. (28 treats the boxes as labelled.)
Answer: C) 7

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