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Question: How many ways can 10 identical buttons, 10 identical bows, and 10 identical beads be distributed to 4 different people?

My thoughts: I decided to use the bars and stars method. With the knowledge that there are 4 unique groups of people, each person has the possibility of getting 1 of the 10 buttons, 1 of the 10 bows, and 10 of the 10 bows. I'm having trouble deciding whether the items are the elements or the actual people are the elements (the stars in this case). Your thoughts?

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Count how many ways there are to distribute $10$ identical buttons between the four people.

Separately count how many ways there are to distribute $10$ identical bows between the four people.

Separately count how many ways there are to distribute $10$ identical beads between the four people.

Apply multiplication principle.

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  • $\begingroup$ After reading it from another person, I'm confident the answer is correct. I wasn't sure if I was thinking correctly when I decided to do \binom{13}{10} = 286 and taking the result and raising it by 3. 286^{3} = 23393656. Thanks! $\endgroup$ – Le Sunstrike Oct 16 '15 at 21:24

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