How many computer passwords can be created with three digits followed by three letters if the first number cannot be 0 or no number or letter can be repeated?
9*9*8 * 26*25*24 = 10108800
To calculate the number of computer passwords that can be created with three digits followed by three letters, we can break down the problem into separate steps:
Step 1: Calculate the number of options for the first digit
Since the first digit cannot be 0, we have 9 options (1-9).
Step 2: Calculate the number of options for the second digit
Since no number can be repeated, we have 9 options again, excluding the number already chosen for the first digit.
Step 3: Calculate the number of options for the third digit
Similarly, we have 8 options for the third digit, since no number can be repeated.
Step 4: Calculate the number of options for the first letter
Since no letter can be repeated, we have 26 options (A-Z).
Step 5: Calculate the number of options for the second letter
Similarly, we have 25 options for the second letter, as we exclude the letter already chosen for the first letter.
Step 6: Calculate the number of options for the third letter
Finally, we have 24 options for the third letter since no letter can be repeated.
Step 7: Multiply the number of options together
To calculate the total number of unique password combinations, we multiply all the options together:
9 * 9 * 8 * 26 * 25 * 24 = 93,312,000
Therefore, there are 93,312,000 possible computer passwords that can be created with three digits followed by three letters without any number or letter repeated.