Avoiding Your Spouse at a Bridge Party
2001; Taylor & Francis; Volume: 74; Issue: 1 Linguagem: Inglês
10.1080/0025570x.2001.11953030
ISSN1930-0980
Autores Tópico(s)History and Theory of Mathematics
Resumo(This problem was first proposed by the mathematician Pierre Remond de Montmort [6], [7]. A more complete discussion of it appears in this MAGAZINE in an article by Gabriela Sanchis [8] and in the excellent history of probability by Anders Hald [5]. It is also discussed in Brawner's article [1].) The well-known solution to this problem iS hn = EyO (-1j' which converges rapidly to e-l. The difference between this classical problem and the bridge couples problem is that in the bridge couples problem, it makes sense for one man to be paired with another, but in the hat matching problem, no man is going to select another man in place of his hat. In this note, I derive a nonrecursive formula for the bridge couples probabilities, and provide a simple approximation formula for computing these probabilities as well as a procedure for getting the exact probabilities to an arbitrary number of decimal places. We use the inclusion-exclusion principle from probability and properties of alternating series to find the nonrecursive formula and establish its limit as n, the number of couples, tends to infinity. Let bn be the probability that of n couples, no one is assigned his or her spouse as a bridge partner.
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