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Enumerating Row Arrangements of Three Species

by Michael Avidon, Richard Mabry and Paul Sisson

This article originally appeared in:
Mathematics Magazine
April, 2001

Subject classification(s): Discrete Mathematics | Combinatorics
Applicable Course(s): 2.7 Finite Math | 3.7 Discrete Math | 4.4 Combinatorics

In how many ways can a pet photographer pose \(C\) cats, \(D\) dogs, and \(E\) emus? The problem, often called Smirnov`s problem,  has several practical applications and has been solved in a variety of ways. The authors present a solution which, unlike previous solutions, is entirely elementary and accessible to students in a first course in combinatorics.

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