Problem1 Illinois license plates must have 4 Arabic numerals

Problem1 Illinois license plates must have 4 Arabic numerals (0 through 9) and 3 phonetic letters (A through Z). How many uniquely registered cars can there be in the state of Illinois?

Solution

There will be total of 7 places in license plate:

4 places for numerals

3 places for letters

Each of 4 places for numerals can have 10 options ( i.e. any number from 0 to 9 )

Each of 3 places for letters can have 26 options ( i.e. , any number from A to Z )

Therefore ,

Possible combinations which can fill in 7 places in number plate

= 10 x 10 x 10 x 10 x 26 x 26 x 26

= 175760000

NUMBER OF UNIQUELY REGISTERED CARS IN ILLINOIS = 175760000

NUMBER OF UNIQUELY REGISTERED CARS IN ILLINOIS = 175760000