A computer password is required to be 7 characters long. How many passwords are possible if the password requires 2 letter(s) followed by 5 digits (numbers 0-9), where no repetition of any letter or digit is allowed?
Possible 2 letters: 26*25
possible 5 digits : 10*9*8*7*6
so possible passwords = 26*25*10*9*8*7*6
= ....
To calculate the number of passwords possible, we need to consider the number of choices for each character in the password.
For the first letter, we have 26 options (since there are 26 letters in the alphabet).
For the second letter, we have 25 options (since we cannot repeat the first letter).
For the third digit, we have 10 options (since there are 10 digits from 0 to 9).
For the fourth digit, we have 9 options (since we cannot repeat the third digit).
For the fifth digit, we have 8 options.
For the sixth digit, we have 7 options.
For the seventh digit, we have 6 options.
Since we want to find the total number of passwords possible, we need to multiply all these choices together:
26 * 25 * 10 * 9 * 8 * 7 * 6 = 6,588,000
Therefore, there are 6,588,000 possible passwords that satisfy the given requirements.
To find the number of possible passwords, we'll first calculate the number of combinations for the letters and digits, and then multiply them together.
1. Calculation for letters:
Since there are 26 letters in the English alphabet, the first letter can be chosen from 26 options, and the second letter from the remaining 25 options (as repetition is not allowed). Therefore, the number of combinations for the letters is obtained as: 26 * 25.
2. Calculation for digits:
Since there are 10 digits (0-9), each digit can be chosen without repetition. Therefore, we have 10 options for the first digit, 9 options for the second digit, 8 options for the third digit, and so on, until we have only one option for the fifth digit. Therefore, the number of combinations for the digits is obtained as: 10 * 9 * 8 * 7 * 6.
3. Calculation for the whole password:
Now, we can combine the number of combinations for the letters and digits to get the total number of possible passwords. Multiplying the combinations for the letters with the combinations for the digits, we have: (26 * 25) * (10 * 9 * 8 * 7 * 6).
Calculating the expression:
(26 * 25) * (10 * 9 * 8 * 7 * 6) = 650 * 30,240 = 19,656,000
Thus, there are a total of 19,656,000 possible passwords for a 7-character password that requires 2 letters followed by 5 digits without repetition.