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I am trying to calculate password of 10 character that must contain at least:

  • 1 lower case character (26)
  • 1 digit (10)
  • 1 special digit (8)

I did this,I just want to confirm I used the principle correctly.

Here is my answer

44^10 - (26 + 10)^10 - (10 + 8)^10 - (26 + 8)^10 + (26^10 + 10^10 + 8^10)

Thanks in advance

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    By calculate, do you perchance mean: *count* the distinct arrangements? – 2017-01-28

1 Answers 1

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Yes; you are applying the principle of counting "including all, excluding (all but 1), and including (all but 2) again" correctly.

$$(26+10+8)^{10} - \big((26 + 10)^{10} + (10 + 8)^{10} + (26 + 8)^{10}\big) + \big(26^{10} + 10^{10} + 8^{10}\big)$$