The use of the factorial function in computing nPr = n!/(n-r)! or in computing nCr = n!/((n-r)!*r!) has overflow problems when n>170 on a 64-bit machine.
These two functions: Perm(n,r) and Comb(n,r) avoid the overflow problem.
nPr is defined as Perm(n,r) and nCr is defined as Comb(n,r).
If n=171, factorial(n) = Inf on a 64-bit machine.
Therefore, neither P(171,15) nor C(171,15) can be evaluated directly.
Perm(171,15) = 1.6611e33, and
Comb(171,15) = 1.2703e21.
Perm(1000,49) = 3.0256e+146, and
Comb(171,15) = 4.9740e+83.
These two functions are useful in predicting the outcomes of Bernoulli experiments that utilize the binomial distribution.
Lawrence Agbezuge (2021). Combinations without overflow (https://www.mathworks.com/matlabcentral/fileexchange/74034-combinations-without-overflow), MATLAB Central File Exchange. Retrieved .
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