A computer password is required to be 5 characters long. How many passwords are possible if the password requires 1 letter(s) and 4 digits (numbers 0-9), where no repetition of any letter or digit is allowed?
number = 26x10x9x8x7
= 131040
To find out the number of possible passwords, we need to determine the number of choices for each character slot.
First, let's consider the number of choices for the letter slot. Since we are given that one letter is required, we can choose any one of the 26 letters of the English alphabet. Therefore, there are 26 choices for the letter slot.
Now, let's consider the number of choices for each of the four digit slots. Since there are no repetitions allowed, we can select any one of the 10 digits (0-9) for the first slot. Similarly, for the second slot, we can choose any one of the remaining 9 digits. For the third slot, we have 8 choices, and for the fourth slot, we have 7 choices.
To find the total number of possible passwords, we multiply the number of choices for each slot:
Number of passwords = (Number of choices for letter) * (Number of choices for first digit) * (Number of choices for second digit) * (Number of choices for third digit) * (Number of choices for fourth digit)
Number of passwords = 26 * 10 * 9 * 8 * 7
Calculating this expression, we find:
Number of passwords = 12,480
Therefore, there are 12,480 possible passwords if the password requires 1 letter and 4 digits, without any repetition of letters or digits.
To calculate the number of possible passwords, we need to determine the number of options for each character position.
1. For the first character (a letter), there are 26 options (since there are 26 letters in the English alphabet).
2. For the second character (a digit), there are 10 options (since there are 10 digits from 0 to 9).
3. For the third character (a digit), there are 10 options (since there are still 10 digits remaining).
4. For the fourth character (a digit), there are 10 options (since there are still 10 digits remaining).
5. For the fifth character (a digit), there are 10 options (since there are still 10 digits remaining).
To get the total number of possible passwords, we multiply the number of options for each character position:
26 * 10 * 10 * 10 * 10 = 260,000.
Therefore, there are 260,000 possible passwords.