Standard automobile license plates in a country display 1 numbers, followed by 3 letters, followed by 3 numbers. How many different standard plates are possible in this system? (Assume repetitions of letters and numbers are allowed.) Your answer is:

**Step 1:** For the first character, which is a number, there are \(10\) possibilities (digits \(0\) through \(9\)). **Step 2:** For the next 3 characters, which are letters, there are \(26\) possibilities for each letter. Since repetitions are allowed, the total number of possibilities for the 3 letters is \[ 26 \times 26 \times 26 = 26^3. \] **Step 3:** For the last 3 characters, which are numbers, there are \(10\) possibilities for each number. Therefore, the total number of possibilities for these 3 numbers is \[ 10 \times 10 \times 10 = 10^3. \] **Step 4:** Multiply the number of possibilities for each part to find the total number of different standard plates: \[ 10 \times 26^3 \times 10^3 = 10^4 \times 26^3. \] **Step 5:** Calculate the value of \(26^3\): \[ 26^3 = 26 \times 26 \times 26 = 17576. \] **Step 6:** Then, compute the final total: \[ 10^4 \times 17576 = 10000 \times 17576 = 175760000. \] **Answer:** \(175760000\)