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I have a set of 71 ASCII characters that I use to assemble 192 character tokens.

I need to calculate the number of permutations (as characters can repeat). The factorial of 192 is so large my computer kacked on it after $$10^{303}$$.

I tried this formula: $$(_{71}P_{71}) x (_{71}P_{71}) x (_{71}P_{50})$$ and came up with $$1.2040547673 x 10^{286}$$.

Is that the right way to calculate this? Is there a better way to calculate $$P(_n, _k)$$ when K is larger than N?

Thank you for your time.

TorontoJim
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    Why isn't the number of character tokens just $71^{192}?$ Aren't there $71$ choices for each of the $192$ characters? $P_{n,k}$ is only used when symbols are not allowed to repeat. This means $P_{n,k}=0$ when $k$ is larger than $n$. – Mike Earnest Oct 10 '17 at 22:06
  • There are only 71 characters. I'm randomizing them into tokens that are 192 characters long. Any individual character can appear multiple times or zero times. I ran a test the other day using my procedure to create 20,000,000 tokens. There were no duplicates. I'm just trying to figure out what the number of tokens is that can be created from all possible randomized assembly of the characters. – TorontoJim Oct 11 '17 at 23:32
  • @MikeEarnest it finally dawned on me today what you were saying. Thank you for your answer ... and patience. – TorontoJim Oct 12 '17 at 21:07

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