Many states offer personalized license plates. California, for example, allows personalized plates with seven spaces for numerals or letters, or one of the following four symbols.


What is the total number of license plates possible using this counting scheme? (Assume that each available space is occupied by a numeral, letter, symbol, or space. Give the answer in scientific notation. Round the first number to two decimal places.)
1 10 2
0

To determine the total number of license plates possible using this counting scheme, we need to calculate the number of choices for each space and multiply them together.

In this case, each space can be filled with a numeral, letter, symbol, or left blank (space). Let's break down the counting options for each space:

1st space: 37 choices (26 letters + 10 numerals + 4 symbols + 1 space)
2nd space: 37 choices
3rd space: 37 choices
4th space: 37 choices
5th space: 37 choices
6th space: 37 choices
7th space: 37 choices

To calculate the total number of license plates possible, we multiply all these options together:

Total = 37 * 37 * 37 * 37 * 37 * 37 * 37

Using a calculator or a programming language, we calculate this value to be:

Total ≈ 1.05 × 10^12

Rounding the first number (1.05) to two decimal places, we get:

Total ≈ 1.05 × 10^12

Therefore, the total number of license plates possible using this counting scheme is approximately 1.05 × 10^12 in scientific notation.