Step 1 :The problem is asking for the total number of different standard plates possible in a given system. The system is defined as having 3 numbers, followed by 3 letters, followed by 1 number.
Step 2 :Since repetitions of letters and numbers are allowed, we can use the multiplication principle of counting. The multiplication principle states that if there are m ways to do one thing, and n ways to do another, then there are m*n ways to do both.
Step 3 :For the numbers, there are 10 possibilities (0-9) for each of the 4 slots. For the letters, there are 26 possibilities (A-Z) for each of the 3 slots.
Step 4 :So, the total number of different standard plates is \(10^4 * 26^3\).
Step 5 :After calculating the above expression, we get the total number of different standard plates possible in this system.
Step 6 :Final Answer: The total number of different standard plates possible in this system is \(\boxed{175760000}\).