How many 4-character license plates are possible with 2
letters from the alphabet followed by 2 digits, if repetitions
are allowed? if repetitions are not allowed?
To find the number of possible license plates, we need to consider whether or not repetitions are allowed.
If repetitions are allowed:
For the first two characters, we can choose any letter from the alphabet, allowing for 26 options each. For the last two characters, we can choose any digit from 0 to 9, allowing for 10 options each. Since repetitions are allowed, the number of possible license plates is the product of these choices: 26 options for the first letter, 26 options for the second letter, 10 options for the first digit, and 10 options for the second digit. Thus, the total number of possible license plates is:
26 * 26 * 10 * 10 = 67,600
If repetitions are not allowed:
For the first letter, we have 26 options. For the second letter, we have 25 options (since we cannot repeat the first letter). For the first digit, we have 10 options. For the second digit, we have 9 options (since we cannot repeat the first digit). Therefore, the total number of possible license plates without repetitions is:
26 * 25 * 10 * 9 = 58,500.