Question

1. A state is considering adding another character to their vehicle license plates in order to increase the number of license plates available. Currently, a license plate must have exactly six character spaces. Each character space may be filled with any capital letter other than I or O or any number between, and including, 0 to 9. Letters and numbers may repeat on the plates.

(a) How many different license plate numbers are available under the current structure of exactly six characters per plate? Show your work.
(b) If the state required all license plates to have exactly seven characters instead of six, how many different license plate numbers would be available with the additional character requirement? Show your work.
(c) How many times bigger is the set of license plate numbers with exactly seven characters than that with the set of six characters? Show your work.
Answer:

Answer 1

9514 1404 393

Answer:

a) 1,544,804,416

b) 52,523,350,144

c) 34

Explanation:

(a) Each character position can be any of 24 letters or 10 digits, so any of 34 characters. The number of possible characters sets increases by a factor of 34 for each added character. A six-character plate will have ...

34^6 = 1,544,804,416 . . . possibilities

__

(b) 34^7 = 52,523,350,144 . . . possibilities

__

(c) 34^7/34^6 = 34 . . . times as many