How many different vehicle licence plates can be made if the licences contain 2 letters of the English alphabet followed by a three digit number if repetitions are allowed?

Options

A. 54320
B. 67534
C. 23456
D. 575324

Answer

To solve the problem of how many different vehicle license plates can be made with the given conditions, we can break it down into steps:

### Step 1: Determine the number of letters
The license plate consists of 2 letters from the English alphabet. Since there are 26 letters in the English alphabet and repetitions are allowed, we can choose each letter independently.

- For the first letter, there are 26 options.
- For the second letter, there are also 26 options.

Thus, the total number of combinations for the letters is:
\[ 26 \times 26 = 676 \]

### Step 2: Determine the number of digits
Next, we need to create a three-digit number. The digits can range from 0 to 9, giving us a total of 10 digits. However, since we are forming a three-digit number, we cannot have a leading zero (i.e., the first digit cannot be 0).

- For the first digit, we can choose from 1 to 9 (9 options).
- For the second digit, we can choose from 0 to 9 (10 options).
- For the third digit, we can also choose from 0 to 9 (10 options).

Thus, the total number of combinations for the digits is:
\[ 9 \times 10 \times 10 = 900 \]

### Step 3: Calculate the total number of license plates
Now, we combine the number of combinations for the letters and the digits to find the total number of different vehicle license plates.

\[ \text{Total combinations} = (\text{Combinations of letters}) \times (\text{Combinations of digits}) \]
\[ = 676 \times 900 \]

Calculating this gives:
\[ 676 \times 900 = 608400 \]

### Final Answer
Thus, the total number of different vehicle license plates that can be made is **608400**.

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