Q&A

# You're sampling k people from a population of size n one at a time, with replacement and with equal probabilities. Order or not?

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If you're sampling k people from a population of size n one at a time, with replacement and with equal probabilities, then why does it matter whether your samples are ordered? The quotation below doesn't expound the pros and cons of ordering your samples or not.

1.4.23. The Bose-Einstein result should not be used in the naive definition of probability except in very special circumstances. For example, consider a survey where a sample of size k is collected by choosing people from a population of size n one at a time, with replacement and with equal probabilities. Then the $n^k$ ordered samples are equally likely, making the naive definition applicable, but the $\dbinom{n + k -1}{k}$ unordered samples (where all that matters is how many times each person was sampled) are not equally likely.

Blitzstein. Introduction to Probability (2019 2 ed). p 20.

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