Restricted Choices

Abstract

A subset consisting of k elements chosen, from n distinct ordered elements, with given restrictions is called are stricted choice. For example, one restriction on the k elements may be that no two consecutive elements appear, while another may be that no two alternate elements appear. Certain restricted choices may be used to obtain solutions to permutation problems ([1, p. 349]; [4]). Each restricted choice corresponds to a "restricted sequence of Bernoulli trials" as described in [1], In this paper an elementary method of obtaining more general types of restricted choices is given. Some special cases of the restricted choices and restricted Bernoulli trials are presented in the form of examples.