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.

Question

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.)

Answer 1

Assume upper case only, gives 26 letters.
Add 10 digits, 1 space and 4 symbols.
Total 26+10+1+4=41 possible symbols.
Subtract the plate that has all spaces.
This is a 7 part experiment each with 41 outcomes, so the total number of possible plates is
N=41^7-1
=194754273880
I will let you do the rounding and the conversion to scientific notation.