Suppose we are given a bag of $n$ identical red balls, what is the number of ways of choosing $3$ red balls from the bag? I know the answer is $$ \binom n3 $$ but isn't there just one way of choosing $3$ balls? They're all identical anyway, so it shouldn't matter! What am I missing here?
2026-04-13 18:00:35.1776103235
Number of ways of choosing identical balls
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The question is poorly worded. The number of ways of choosing a set of three balls from the bag is $\binom{n}3$; if the balls are truly identical, however, the number of distinguishable outcomes is, as you say, just $1$. If the former answer is intended, the inclusion of the words identical red is misleading at best. If the latter answer is intended, this should be clearer, for instance by adding the word distinguishable, as I did above.