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It's basic binomial probability, the problem is that the numbers are to large for my calculator. Is this the point of the task, to force me to use another method? It doesn't seem lightly, because n over r is a must anyways. An example would be 1000 over 180.

Note that on the exam it self I am allowed to use my laptop (mac), but not the net. So if you can think of any programs that can deal with this size of numbers I'd appreciate it.

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    Is the problem you are solving related to the binomial distribution? If so, there is the normal approximation(http://en.wikipedia.org/wiki/Binomial_distribution#Normal_approximation) and the Poisson approximation (http://en.wikipedia.org/wiki/Binomial_distribution#Poisson_approximation). I am suggesting this in a comment because it doesn't directly answer your question as stated.2011-07-22

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You can use Stirling's approximation to get the logs of the factorials. So if $x_k={1000\choose k}0.2^k0.8^{1000-k}=\frac{1000!}{k!(1000-k)!}0.2^k0.8^{1000-k}$ you have $\log x_k\approx (1000+\frac{1}{2})\log 1000-(k+\frac{1}{2}) \log k - (1000-k+\frac{1}{2})\log (1000-k)$ $ -\frac{1}{2}\log 2\pi+k \log 0.2 + (1000-k) \log 0.8$

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Since I'm allowed to use my computer the bcd function on my casio can be done in excel with the following line: =BINOMDIST(180,1000,0.2,TRUE). The true part is because we want the probability for at most 180 people/success.

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    I got in contact with the author and we are allowed to use laptops on the exam. Problem solved.2011-09-10