##
**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 |

Full Text:
DOI

### References:

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.