## 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.

### MSC:

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

### Keywords:

Catalan numbers; sock matching; Dyck paths
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