... =12342143,indicating that a1went to a2, a2 to a1, a3 to a4, and a4 to a3.Ifwealwayschoosethetoprowtobe1234then, to prescribe the permutation,we need only give the bottom row, with the understanding ... Birthday problem.We now turn to the topic of permutations.PermutationsDefinition 3.1 Let A be any finite set. A permutation of A is a one -to- one mappingof A onto itself. ✷ To specify a particular ... sent by the one -to- one mapping. For example, if A ={a, b, c} a possible permutation σ would beσ =abcbca.By the permutation σ, a is sent to b, b is sent to c, and c is sent to a. Thecondition...