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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 can calculate I have ~ $3.2333\mathtt E+19$ possible combinations

However, if I change one of the requirements to at least TWO digits $0-9$, how can I calculate the possible combinations?

  • 4
    By inclusion-exclusion again. There are just more terms.2010-08-27
  • 0
    You can take your previous answer, compute the number of passwords that had exactly one digit, and subtract it.2010-08-27
  • 0
    So since there are 3.2333E+19 possible combinations remaining, and each of those has at least 1 digit, and the most digits it can have is 7, wouldn't the answer be 6/7's of the 3.2333E+19 = 2.77143E+19?2010-08-27

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