Question

How many different six-place license plates are possible if the first three places and the last place are to be occupied by letters and the fourth and fifth places are to be occupied by numbers?

Answer 1

26³10²36

Explanation:

We use the product rule: to find all the possibilities for a plate, we count all the possibilities for each one of the 6 places on a plate. I will assume you can use any of the 26 letters of the English alphabet and the digits 0,1,...,9.

The 1st, 2nd and 3rd places of the plate must be occupied by any of the 26 letters. The 1st place has 26 possibilities, the 2nd has 26 possibilities and the 3rd has 26 possibilities, hence there are 26×26×26=26³ possibilities for the first 3 places.

Similarly, the 4th and 5th places have a total of 10×10=10² possibilities. The last position has 36 possibilities, because it can be either a letter or a number.

Therefore, the number of possible plates is 26³10²36