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Counting Derangements, Non Bijective Functions and the Birthday Problem

DOI: 10.2478/v10037-010-0023-9

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The article provides counting derangements of finite sets and counting non bijective functions. We provide a recursive formula for the number of derangements of a finite set, together with an explicit formula involving the number e. We count the number of non-one-to-one functions between to finite sets and perform a computation to give explicitely a formalization of the birthday problem. The article is an extension of [10].


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