The sock matching problem. (English) Zbl 1297.05019

Summary: When matching socks after doing the laundry, how many unmatched socks can appear in the process of drawing one sock at a time from the basket? By connecting the problem of sock matching to the Catalan numbers, we give the probability that \(k\) unmatched socks appear. We also show that, for each fixed \(k\), this probability approaches \(1\) as the number of socks becomes large enough. The relation between the number of socks and the \(k\) for which a given probability is first reached is also discussed, but a complete answer is open.


05A15 Exact enumeration problems, generating functions
05A16 Asymptotic enumeration
60C05 Combinatorial probability
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