of possible ways of dividing the set. The relation between these two models is described in the following table: This relation let us transform the table provided by the distribution model into a new one that can be used to know the different ways of dividing a set of k elements into n subsets: Examples 1.- A group of 3 classmates have to make a thesis about 8 different maths topics. In how many ways can they split the work to do? We need to divide the set of 8 topics into 3 subsets. These subsets will be the topics that each of the students will work on. The elements in the set (topics) are distinguishable. The partitions must be ordered because each one will correspond to a different student, but the topics inside every subset do not have to be ordered because each student can decide which order to follow when working on the thesis. The statement does not mention any restriction of the subsets. So, it is required to divide a set of 8 elements () into 3 ordered subsets () of non ordered elements. That is all we need to know to choose the right operation, and the result is: See also Twelvefold way Sources Dubois, Jean-Guy. Une systématique des configurations combinatoires simples. Educational Studies in Mathematics 15, 37–57 (1984) doi:10.1007/BF00380438 V. Navarro-Pelayo; Carmen Batanero; Juan D. Godino (1996). Razonamiento Combinatorio en Alumnos de Secundaria. Rafael Roa (2000). Razonamiento Combinatorio en Estudiantes con Preparación Matemática Avanzada. Tan Mingshu (2011). Some Combinatorial Identities and Explanations Based on Occupancy Model. Combinatorics