Simplifying Binomial Coefficients with large numbers, i.e., factorials of large numbers

#1
Hi, I'm reading a paper about stats in psychology (https://www.ejwagenmakers.com/2007/pValueProblems.pdf) and there is an equation in there that I cannot work out.

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I'm not a mathematician, but as I understand, the binomial coefficient could be simpified as such:
1000! / 500!(1000!- 500!)

Then, I'd multiply the outcome of that by 0.5^1000. According to the paper (p781), the end result should be "about .025"

However, I'm having difficulty with the initial step because 1000! and 500! give infinite numbers. Is there a simple way of calculating the whole equation to get 0.025?

Many thanks!
Ryan
 
Last edited:

spunky

Doesn't actually exist
#2
Hi, I'm reading a paper about stats in psychology (https://www.ejwagenmakers.com/2007/pValueProblems.pdf) and there is an equation in there that I cannot work out.

View attachment 2836

I'm not a mathematician, but as I understand, the binomial coefficient could be simpified as such:
1000! / 500!(1000!- 500!)

Then, I'd multiply the outcome of that by 0.5^1000. According to the paper (p781), the end result should be "about .025"

However, I'm having difficulty with the initial step because 1000! and 500! give infinite numbers. Is there a simple way of calculating the whole equation to get 0.025?

Many thanks!
Ryan
You're running into a combinatorial explosion problem, which is very typical of discrete mathematics.

But it shouldn't be too difficult to simplify the expression to something you can evaluate. If you're unfamiliar with how to simplify factorial ratios, here's something to get you started: