Question

California is coming out with a new license plate. The license plate will have 2 letters followed by 3 digits from 0 to 9 then followed by another letter. How many different license plates are possible if no letters and no digit repeat?

Answer 1

11,232,000 different plates

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