%0 Journal Article
%T Counting Derangements, Non Bijective Functions and the Birthday Problem
%A Cezary Kaliszyk
%J Formalized Mathematics
%@ 1898-9934
%D 2010
%I 
%R 10.2478/v10037-010-0023-9
%X 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].
%U http://versita.metapress.com/content/a65303w82q772122/?p=9ae4ba60c935434f835f9c59f251df83&pi=1