Answer:
11,232,000 different plates
Step-by-step explanation:
Figure it out like this:
2letters × 3digits × 1letter
Nothing can repeat. There are 26 letters in the alphabet. If we use 1 of those letters, then there are only 25 letters left to choose from. That's why we start with 26 × 25.
Now for the digits, we have 10 choices for the first digit, then 9 choices for the second digit, then 8 choices for the third digit. That's why we follow the letters with 10 × 9 × 8.
For the last letter, we had 24 choices left, so the whole thing is found by multiplying:
26 × 25 × 24 × 10 × 9 × 8 × 24 = 11,232,000
