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Suppose that passwords for an email provider: must be either 8 or 10 characters long are...

Suppose that passwords for an email provider:

  • must be either 8 or 10 characters long
  • are case-sensitive, can include digits, and can include any of 12 special characters
  • cannot end in a special character
  • must contain at least one capital letter, one digit, or one special character (can contain more than one, just must contain at least one)

How many different passwords are possible?   Show your work.   Work on the back of this sheet and attach additional sheets as necessary.    A final answer in combinatorial is acceptable.

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