Question

A license plate is to consist of 3 letters followed by

33

digits. Determine the number of different license plates possible if the first letter must be an​ K, L, or M and repetition of letters and numbers is not permitted.

A.

1 comma 296 comma 0001,296,000

B.

1 comma 386 comma 0001,386,000

C.

9 comma 072 comma 0009,072,000

D.

162 comma 000

Answer 1

We have to choose 3 letters (out of 26) and 3 digits (out of 9).

1. For the first letter we have 3 choices (K, L, M).

2. For the second letter we are left with 25 choices (removing the first letter selected).

3. And hence, for the third letter, we have 24 choices.

4. Now, the first digit can be anything from the 9 digits. So, we have 9 choices.

5. For the next digit, we now have 8 choices.

6. And finally, for the last digit we have 7 choices.

Therefore, total number of ways = 3×25×24×9×8×7 = 907200