The solutions to the exclusive occupancy problem involving the placement of groups of indistinguishable balls

• Main Authors: Liwanag, Ma. Ferlita P., Simbahan, Nenita C.
• Format: text
• Language: English
• Published: Animo Repository 1995
• Subjects: Problem solving; Programming (Mathematics); Combinatorial group theory
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16256
• Institution: De La Salle University

The occupancy problem involved in this study asks for the total number of ways by which the placement of k groups of indistinguishable balls in n linearly arranged cells is accomplished, subject always to the restriction that the members of each of the k groups occupy adjacent cells with only one ball per cell. Here, two particular situations will be considered and analyzed. First is the situations wherein the groups involved are all of the same size. Second is the situation wherein groups vary in sizes. However, in this second case, the results that will be obtained is valid only if the order of the runs is specified. For these two general cases, basic combinatorics and recursions will be used to develop solutions to the specified problem.A computer program that will execute the viable occupancy situations, represented through the seat numbers, is also given in this study.