An Application of Combinatorial Methods

Probability theory is a branch of mathematics concerned with determining the long run frequency or chance that a given event will occur. This chance is determined by dividing the number of selected events by the number of total events possible, assuming these events are equally likely. Probability theory is simply enumerative combinatorial analysis when applied to finite sets. For a given finite sample space, probability questions are usually "just" a lot of counting. The purpose of this thesis is to provide some in depth analysis of several combinatorial methods, including basic principles of counting, permutations and combinations, by specifically exploring one type of probability problem: C ordered possible elements that are equally likely s independent sampled subjects r distinct elements, where r = 1, 2, 3, …, min (C, s) we want to know P(s subjects utilize exactly r distinct elements). This thesis gives a detailed step by step analysis on techniques used to ultimately finding a general formula to solve the above problem.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Mathematical Sciences

Year dc:date.available

2005

Author dc:creator

• Yang, Yingying

Contributors dc:contributor

• Dr. D'Arcy P. Mays

• Probability Theory
• enumerative combinatorial analysis
• finite sets
• Physical Sciences and Mathematics

Statement dc:rights

• © The Author

Identifier

https://scholarscompass.vcu.edu/etd/662

OAI identifier oai:identifier

oai:scholarscompass.vcu.edu:etd-1661