If I create a 10 digit password with the following requirements: At least one uppercase letter

Jaydan Aguirre

Jaydan Aguirre

Answered question

2022-07-13

If I create a 10 digit password with the following requirements:
At least one uppercase letter A-Z: 26
At least one lowercase letter a-z: 26
At least one digit from 0 9: 10
At least one common symbol ( ( # , $ , % , etc): 32
By inclusion-exclusion, I have ~ 3.2333 E + 19 possible combinations
However, if I change one of the requirements to at least two digits 0 9, how can I calculate the possible combinations?

Answer & Explanation

Ashley Parks

Ashley Parks

Beginner2022-07-14Added 11 answers

You have to choose 10 letters, and 2 of them must be digits. Furthermore, there must be one each of a lowercase letter, an upper case letter, and a common symbol. For the others, there are 5 choices to be made, and these are to be made from 26 + 26 + 10 + 32 = 94 characters.
This gives
94 5 7.339 e 9
choices for the the 6 other characters that do not have to be digits. And for the digits, there are 2 choices from 10 characters. So this gives
10 2 = 100
choices. And for the one each of lower-case letters, upper-case letters, and common symbols there are
26 26 32 = 21632
choices.
Now lastly, there are 10 ! permutations of these 10 characters, so the total number of combinations of these characters is:
26 26 32 100 94 5 10 ! 5.76 e 22

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