a license plate is to consist of three digits followed by two uppercase letters. determine the number of different license plates possible. the first digit cannot be zero and repition is not permitted.
I don't see why the first digit cannot be zero. Is having a three digit number like 101 considered repetition?
To determine the number of different license plates possible, we need to consider the requirements mentioned:
1. The license plate should consist of three digits followed by two uppercase letters.
2. The first digit cannot be zero, so it can be any number from 1 to 9.
3. Repetition is not permitted; each digit and letter should be unique.
Let's break down the calculation step-by-step:
Step 1: Count the possibilities for the first digit.
Since the first digit cannot be zero, there are nine possible choices (1-9).
Step 2: Count the possibilities for the second and third digits.
After choosing the first digit, we have eight remaining digits to choose from for the second digit and seven for the third digit (since no repetition is allowed).
Step 3: Count the possibilities for the uppercase letters.
There are 26 uppercase letters in the English alphabet. Since repetition is not allowed, each letter can only be used once. For the first letter, we have 26 choices, and for the second letter, we have 25 choices.
Step 4: Calculate the total number of possibilities.
To find the total number of possibilities, multiply the choices from each step together:
9 choices for the first digit * 8 choices for the second digit * 7 choices for the third digit * 26 choices for the first letter * 25 choices for the second letter.
So, the number of different license plates possible is:
9 * 8 * 7 * 26 * 25 = 327,600.