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Dinner-Diner Matching Probabilities

Consider a banquet at which *n* different entrees are
served and *k* guests have requested each entree. Suppose the dinners are
served randomly to the diners. What is the distribution of the number of matches
of dinners to the diners who ordered them?

The following graphs illustrate the relationship between the
dinner-diner matching probabilities and the normal distribution, and the relationship
between the dinner-diner matching probabilities and the Poisson distribution.
Sequence numbers refer to sequences listed in N. J. A. Sloane (2000), The On-Line
Encyclopedia of Integer Sequences, published electronically at
http://www.research.att.com/~njas/sequences/. The integer sequences are
the numerators of the discrete probability distributions, laid out in triangular
arrays.

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