Question

how many different license plates are possible if every license plate has 3 capital letters followed by 3 numeric digits, assuming that letters and digits can NOT be repeated? (e.g., ABA 325 is NOT valid, but ABC 325 is valid)

Answer 1

There are 11,232,000 different license plates possible if every license plate has 3 capital letters followed by 3 numeric digits, assuming that letters and digits cannot be repeated.

Step-by-step explanation:

To calculate the number of different license plates that are possible, we need to determine how many choices there are for each character slot.

There are 26 letters in the alphabet and 10 digits, so for the first character slot, there are 26 choices. Since digits and letters can't be repeated, for the second character slot, there are 25 choices.

And for the third character slot, there are 24 choices. Similarly, for the fourth, fifth, and sixth character slots, there are 10, 9, and 8 choices respectively. To find the total number of possibilities, we multiply all these choices together:

Total number of license plates = 26 * 25 * 24 * 10 * 9 * 8 = 11,232,000