To calculate the number of 6-symbol license plates of this format that can be created in Missouri, you can use the multiplication principle (also known as the counting principle).
1. For the first symbol, you can choose any letter of the alphabet, so there are 26 options.
2. Similarly, for the second symbol, there are 26 options.
3. For the third symbol (a digit), you can choose any digit from 0 to 9, so there are 10 options.
4. The fourth symbol (a letter) again has 26 options.
5. The fifth symbol (a digit) has 10 options.
6. Finally, for the sixth symbol (a letter), there are 26 options.
To find the total number of possible license plates, multiply the number of choices for each symbol together:
26 (1st symbol) * 26 (2nd symbol) * 10 (3rd symbol) * 26 (4th symbol) * 10 (5th symbol) * 26 (6th symbol) = 26^4 * 10^2
Calculate the result:
26^4 = 26 * 26 * 26 * 26 = 456,976
10^2 = 10 * 10 = 100
Now, multiply these two results together:
456,976 * 100 = 45,697,600
So, there are 45,697,600 possible 6-symbol license plates of this format in Missouri when there are no other restrictions.