How many 5-character license plates are possible with 2 letters from the alphabet followed by 3 digits, if repetitions are allowed?
if repetitions are not allowed?
clearly 26x26x10x10x10
assuming that the zero can be used.
Thank you for your help.
To find the number of 5-character license plates possible with 2 letters from the alphabet followed by 3 digits, if repetitions are allowed, we need to consider the number of choices available for each character.
For the first letter, there are 26 choices (since there are 26 letters in the alphabet). For the second letter, again there are 26 choices available. For the three digits, there are 10 choices (since there are 10 digits from 0 to 9).
Since repetitions are allowed, the number of possible plates is equal to the number of choices for each character multiplied together. Therefore, the total number of 5-character license plates possible is:
26 choices for the first letter * 26 choices for the second letter * 10 choices for the first digit * 10 choices for the second digit * 10 choices for the third digit
Therefore, the total number of 5-character license plates possible with repetitions allowed is 26 * 26 * 10 * 10 * 10 = 676,000.
Now, let's consider the case where repetitions are not allowed. In this case, once a character is chosen, it cannot be repeated in the remaining characters.
For the first letter, there are 26 choices. For the second letter, there are 25 choices (since we cannot choose the same letter as the first letter). For the three digits, there are 10 choices for each digit.
Therefore, the total number of 5-character license plates possible with repetitions not allowed is:
26 choices for the first letter * 25 choices for the second letter * 10 choices for the first digit * 10 choices for the second digit * 10 choices for the third digit
So the total number of 5-character license plates possible with repetitions not allowed is 26 * 25 * 10 * 10 * 10 = 650,000.