SOLUTION: A computer password consist of a letter of the alphabet followed by 3 or 4 digits.Find the total number of password that can be formed. Also find the number of passwords in which n

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Question 1010649: A computer password consist of a letter of the alphabet followed by 3 or 4 digits.Find the total number of password that can be formed. Also find the number of passwords in which no digit repeats.
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
Digits can repeat:

Case 1.  1 letter followed by 3 digits
Choose the letter 26 ways.
Choose the first digit 10 ways.
Choose the second digit 10 ways.
Choose the third digit 10 ways.

That's 26*10*10*10 = 26000

Case 2. 1 letter followed by 4 digits.
Annex a digit to each of the 26000 ways in Case 1.
That can be done in 10 ways.
That's 26000*10 = 260000

Grand total: 26000 + 260000 = 286000

---------------------------

Digits cannot repeat:

Case 1.  1 letter followed by 3 digits
Choose the letter 26 ways.
Choose the first digit 10 ways.
Choose the second digit 9 ways.
Choose the third digit 8 ways.

That's 26*10*9*8 = 18720

Case 2. 1 letter followed by 4 digits.
Annex a fourth digit to each of the 18720 ways in Case 1.
That can be done in 7 ways.
That's 18720*7 = 131040

Grand total: 18720 + 131040 = 149760

Edwin
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