Combinatorics and Campus Security (UMAP)

One day I received electronic mail from our director of campus security [Gilbraith 1993]: I have a puzzle for you that has practical applications for me. I need to know how many different combinations there are for our combination locks. A lock has 5 buttons. In setting the combination you can use only 1 button or as many as 5. Buttons may be pressed simultaneously and/or successively, but the same button cannot be used more than once in the same combination. I had a student (obviously not a math major) email me that there are only 120 possibilities, but even I know this is only if you press all five buttons one at a time. It doesn't take into account 1-23-4-5, for instance. My question to you is how many combinations exist, and is it enough to keep our buildings adequately protected?

Table of Contents:

INTRODUCTION

GENERATING FUNCTIONS

ASYMPTOTICS

ACKNOWLEDGMENT

REFERENCES

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