Generalization of Some Problems with <i>s</i>-Separation

Abstract

In this article we apply and discuss El-Desouky technique to derive a generalization of the problem of selecting k balls from an n -line with no two adjacent balls being s -separation. We solve the problem in which the separation of the adjacent elements is not having odd and even separation. Also we enumerate the number of ways of selecting k objects from n -line objects with no two adjacent being of separations m , m + 1 , … , pm, where p is positive integer. Moreover we discuss some applications on these problems.