Question

If an Ohio license plate can have have 7 possible spaces composed of letter, numbers, and a space, where repetition is allowed, how many different license plates can there be in all of Ohio? Please show all work

Answer 1

Given 7 spaces, each space can consist of a letter (26 letters in the alphabet), a number (numbers 0 to 9: for a total of 10 numbers), and a space (1).

Adding the amount of letters, numbers, and a space equals:
26 + 10 + 1 = 37 possible characters for each space on the license plate.

Since repeat characters are allowed, each space can have 37 possible characters.

The plate has 7 spaces so:
37 x 37 x 37 x 37 x 37 x 37 x 37
= 37^7 different combinations.