SOLUTION: 1. A password must be 6, 7, or 8 characters long, and may include capital letters, lower-case letters, or digits. In how many ways could this be done a. with no r

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Question 950549: 1. A password must be 6, 7, or 8 characters long, and may include capital letters, lower-case letters, or digits. In how many ways could this be done

a. with no restriction?

b. with no repetition permitted?

c. if at least one of the characters in part a) must be a digit?
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
1. A password must be 6, 7, or 8 characters long, and may include capital
letters, lower-case letters, or digits. In how many ways could this be done

a. with no restriction?
26 capital letters + 26 lower case letters + 10 digits = 62 characters

62^6 + 62^7 + 62^8 = 221918520426688

b. with no repetition permitted?
62P6 + 62P7 + 62P8 = 138848807594160

c. if at least one of the characters in part a) must be a digit?
That will be the answer to (a) minus the number with no digits.

With no digits:

26 capital letters + 26 lower case letters = 52 characters

52^6 + 52^7 + 52^8 = 54507570843648

Subtracting from the result of part (a)

221918520426688 - 54507570843648 = 167410949583040

Edwin
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