#### Title

#### Date of Award

5-1-2013

#### Degree Name

Master of Science

#### Department

Mathematics

#### First Advisor

Calvert, Wesley

#### Abstract

A classic combinatorics problem is: What is the probability that if n people randomly reach into a dark closet to retrieve their hats, no person will pick his own hat? Now there are n! ways to retrieve n hats if you didn't care which hat you got. But for this problem you need to determine how may different ways no person will pick his own hat. In this paper we expand on the original idea and consider two variations of this problem: If there are n elements and m distinguishable possibilities, in how many ways can you rearrange these elements. For example, if n men check their hats and k women check their hats, in how many ways will the men retrieve a different hat than the one he checked. The second problem is: if n people randomly reach into a dark closet to retrieve their hat but now there are m hats in the closet, how many different ways will no person retrieve his hat? In the second case m >= n.

#### Access

This thesis is only available for download to the SIUC community. Others should

contact the interlibrary
loan department of your local library.