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?

Answer 1

Well, let's see if i got it right.
You have 9 different letters and 3 spots, no repeating, different order means different combination (right?).
Let's see how many cases we have.
For first spot we have 9 different cases, for any one of those letters as the first one.
For second spot, no matter what letter was first, there are 8 others that could fit in, so that makes it 8 cases for each one of the cases above.
So far 9*8.
Third place has same idea, 7 other letters could fit in in any one of the cases above, so 9*8*7
8*7 = 56
56 * 9 = 560 - 56 = 504

Hope that's right