Suppose I have some i.i.d. random variables $X_1,\dots,X_{n}$ which represent the $nth$ balls drawn uniformly from a bin without replacement. Is sampling without replacement a condition that is put on the set I define my probability measure on? In that all elements $w\in \Omega$ are such that they do not have repeated draws? Or is it a property of the random variable with which I use to sample?
2026-04-24 19:17:08.1777058228
How are draws without replacement formalized?
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It will be defined by the sample space, since you are only allowing outcomes that have no repeating elements.
So your sample space consists of $K \choose n$ unique selections of balls times $n!$ ways of arranging them or a total size of ${K \choose n}n! $