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:

To calculate the total number of different standard automobile license plates possible, we first break down the components: 1. For the first digit, there are 10 possible numbers (0-9). 2. For each of the three letters, assuming there are 26 letters in the alphabet, there are 26 options per letter. 3. For the last three numbers, it again offers 10 options each. The total combinations would be calculated as follows: (10 options for the first number) * (26 options for the first letter) * (26 options for the second letter) * (26 options for the third letter) * (10 options for the first number) * (10 options for the second number) * (10 options for the third number). Mathematically, it is: 10 × (26^3) × (10^3) = 10 × 17,576 × 1,000 = 175,760,000. So, the total number of different standard plates possible is 175,760,000.