How do I solve this problem, A license plate consists of 2 uppercase letters followed by 4 digits. If repetition of letters is allowed, and repetition of digits is not allowed, how many different license plates are possible?
There are 26 uppercase letters in the English alphabet and 10 digits (0-9).
For the first letter, there are 26 choices. Similarly, there are 26 choices for the second letter. For the first digit, there are 10 choices. However, for the second digit, we cannot repeat the first digit, so there are only 9 choices. Similarly, for the third digit, there are only 8 choices and for the fourth digit, there are only 7 choices.
Therefore, the total number of possible license plates is:
26 x 26 x 10 x 9 x 8 x 7 = 11,441,600
To solve this problem, we need to break it down into steps.
Step 1: Determine the number of possibilities for the first uppercase letter.
Since repetition of letters is allowed, there are 26 possibilities for the first letter.
Step 2: Determine the number of possibilities for the second uppercase letter.
Similarly, since repetition of letters is allowed, there are 26 possibilities for the second letter as well.
Step 3: Determine the number of possibilities for the first digit.
Since repetition of digits is not allowed, there are 10 possibilities for the first digit. (0-9)
Step 4: Determine the number of possibilities for the second digit.
Similarly, there are 10 possibilities for the second digit.
Step 5: Determine the number of possibilities for the third digit.
Again, there are 10 possibilities for the third digit.
Step 6: Determine the number of possibilities for the fourth digit.
Lastly, there are 10 possibilities for the fourth digit.
Step 7: Multiply the number of possibilities from each step together to find the total number of different license plates possible.
Multiplying the possibilities from each step together:
26 (possibilities for the first letter) * 26 (possibilities for the second letter) * 10 (possibilities for the first digit) * 10 (possibilities for the second digit) * 10 (possibilities for the third digit) * 10 (possibilities for the fourth digit)
= 26 * 26 * 10 * 10 * 10 * 10
= 676,000
Therefore, there are 676,000 different license plates possible.