Combinatorics applications?

Question

Hi everyone. I was wondering if anyone has any ideas of combinatorics application in life that we can explore for a math project, and preferably turn up with some original answers. Thanks loads:)

Answer 1

I'll focus on your phrase "Original Answers."

Project 1
You could consider the limitations and full range of genetic variability. Then you can compare with known vairations and lack thereof, preferably limiting yurself to assessing very few genes. In comparing these numbers you can make strong verifiable statements and inferences about survival and fitness of the different alleles for those phenotypes. I've never heard of a combinatorics approach, which would be relatively simple at first glance [although you'll need to account for benign factors.]

Project2
How many stars are there to be seen in the night sky? You could apply such things as the Pigeon-hole principle to establish minimum and maximum, sticking to combinatorics. If you are allowed to make detailed concluding remarks you could add probability to your assessment, but I'll keep this simple.
Suppose there are n stars visible from the earth, of radius r. A personally viewed horizon covers a circle of radius h. You may now calculate a minimum number of stars that can be guaranteed to be in the horizon of at least m persons' views! Go on!

Answer 2

Protein design might be a good source of problems: assemble any number of the amino acids into a molecule with some desired properties. The problem is quite open. The human and economic pay-offs would be huge.

A less ambition project but still open, is to find stable arrangements of some given molecules. For water, one question is how many forms of ice are there. That question is relevant for cloud formation, which in turn may have an impact on climate modeling.

I would start solving a toy problem first before trying an approach with real data.

Here are a few URLs where you might find some more project ideas.

Answer 3

There is a voting reform concept called the "Australian System", where you get a chance to vote for a second or third choice on a ballot. Why don't you look into it and see some of the logistics of handling it on the voting system used in your state (or county).