I'm really confused about the elevator probability problems. I really appreciate your input. If let's say we have 4 floors and 4 passengers, whats the total way of distribution? I know that it should be 256 (4x4x4x4) since every passenger has 4 options, however, I can't understand why we can't write it like x1 + x2 + x3 + x4 = 4, x<= 4 (as if we have 4 urns (floors) and we need to distribute 4 balls (passengers)) and use in that case the (n + k - 1) choose (k or n - 1) formula which is 7C4 or 7C3. Thanks!
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Does this answer your question? Why is flipping a head then a tail a different outcome than flipping a tail then a head? – JMoravitz Jan 27 '20 at 17:41
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1TLDR: We have a choice. Both are valid answers to the question, but which you wish to use depends on for what purpose you are wanting the answer. Typically, the first would be preferred since it leads to an equiprobable sample space so that we can more easily discuss probability questions related to the scenario while the second is not useful for this. – JMoravitz Jan 27 '20 at 17:47
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2Your alternative is correct if we only care how many passengers get off at each floor, but not if we care which passengers they are. – saulspatz Jan 27 '20 at 18:04