- #1

iamjokerface

I am stuck on this one problem. The problem asks:

How many different 7-place license plates are possible when 3 of the entries are letters and 4 are digits? Assume that repetition of letters and numbers is allowed and that there is no restriction on where the letters or numbers can be placed.

The way I approached the problem was:

There are 7C3 ways of choosing the places for letters, and in each letter place, there can be 26 choices. So 7C3*26*26*26 for the letters.

Then there are 7C4 ways of choosing the places for digits, and in each digit place, there are 10 choices, so 7C4*10*10*10*10.

To get the total possibilities, I multiplied the two.

I checked the answer but I am not getting the correct answer.

Where have I gone wrong?