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I am trying to figure out the maximum possible combinations of a (HEX) string, with the following rules:

  • All characters in uppercase hex (ABCDEF0123456789)
  • The output string must be exactly 10 characters long
  • The string must contain at least 1 letter
  • The string must contain at least 1 number
  • A number or letter can not be represented more than 2 times

I am thinking the easy way to go here (I am most likely wrong, so feel free to correct me):

  1. Total possible combinations: $16^{10} = 1,099,511,627,776$
  2. Minus all combinations with just numbers: $10^{10} = 10,000,000,000$
  3. Minus all combinations with just letters: $6^{10} = 60,466,176$
  4. etc...

Can someone could tell me if this is the right way to go and if so, how to get the total amount of possible combinations where a letter or a number occur more than twice.

Any input or help would be highly appreciated!

Muchos thanks!

PS.

I don't know if I tagged this question right, sorry :(

DS.

  • 0
    I changed it to combinatorics, which is all about counting things. The thing is, you use combinatorics often in probability, so your choosing of probability wasn't a bad tag. I just thought combinatorics was more accurate. This problem could be done in relation to some probability, or without any relation to probability.2012-02-27
  • 0
    It's not clear if you are counting different combinations (order does not matter) or numbers of strings (order matter)2012-05-01

3 Answers 3