if a license plate has 3 digits and 3 letters how many outcomes are there if digits can be repeated but letters cannot?

Question

Need to see a tree diagram

Answer 1

I'm assuming that it is 3 numbers followed by 3 letters. If not, there are even more possibilities. I'm also including all permuations, This means that --e.g. --321, 312, 213, 231, 123, and 132 all count as different options.

The digits can be repeated, so there are 1000 combinations ( 10 X 10 X 10 )

Since the letters can not be repeated, the number of options is 26 X 25 X 24 = 15,600

So, I get 15,600,000 for the total number of outcomes

Answer 2

You can pick the 3 spaces for the in ₆C₃ ways and fill those spaces in ₆P₃ ways. Then you have 3 spaces to fill each of which can be filed in 10 ways. Therefore, 20*26*25*24*10³. A lot of license plates!