Final answer:
The number of different license plates that can be made without repetition can be calculated using permutations and multiplication. The formula to calculate the number of different plates is 4P2 * 26^4 * 10^2.
Step-by-step explanation:
The number of different license plates that can be made without repetition can be calculated using the concept of permutations. There are 4 letters and 2 numbers, and repetition is not allowed.
The number of ways to arrange the 4 letters in 4P2 ways (4P2 = 4!/(4-2)! = 12).
The number of ways to choose the 2 numbers from the set of 10 numbers is 10P2 (10P2 = 10!/(10-2)! = 90).
Finally, since repetition is not allowed, each letter and number can be chosen from the set of 26 letters and 10 numbers respectively. Therefore, we multiply the number of choices for letters and numbers.
So, the total number of plates that can be made without repetition is 4P2 * 26^4 * 10^2.