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.
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
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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