ABSTRACT
After analyzing combinations and permutations, it may be interesting to examine the operation which is the synthesis of these two and which is generally called arrangement. 2 In the arrangements of two terms A and B, taken in pairs AA, AB, BA, BB, there are, in fact, simultaneously combinations (AA, BB, AB) and permutations (AB and BA). But the study of these arrangements will not simply be a means of allowing us to organize what we have just concluded in our research above; it will also lead us to a correlation which seems to exist between the combinatoric operations and the progress of the idea of chance. In this regard it will be sufficient to study the intentional arrangements made by the child along with his ideas on the resulting fortuitous arrangements, for example, from a random mixture of cards drawn in pairs. Now the exigencies of the analysis led us earlier to dissociate all the following: the study of operations of combinations (Chapter VII), the study of fortuitous combinations (Chapters V and VI), the study of the operations of permutations (Chapter VIII), and those of fortuitous permutations (Chapter I). In the light of these analyses, we will be able to describe simultaneously the reactions of children vis-à-vis operations of arrangements and fortuitous arrangements 1 .
