How many different 3-letter codes are there if only the letters A, B, C, D, E, F, G, H, and I can be used and no letter can be used more than once?

I came up with 3 for this one--wrong! How would I solve?

Question

How many different 3-letter codes are there if only the letters A, B, C, D, E, F, G, H, and I can be used and no letter can be used more than once?

I came up with 3 for this one--wrong! How would I solve?

debbieg · Answer

There are 8 letter choices for each of the 3 "slots" available in the code, but once one letter has been used, it can't be used again.

So for the first letter, there are 8 possibilities....

Then for the 2nd letter, there are 7 possibilities.....

finally 6 for the 3rd letter.

Picture it as a tree diagram. How would you then compute how many branches are at the end?