Hello, arze!

Your answer would be correct if there were 7How many combinations of three letters taken from the letters A,A,B,B,C,C,D are there?letters.different

Because of the duplicated letters, I counted the cases rather primitively.

How many 3-letter combinations have 3 different letters?

There are 4 different letters available, and we pick 3 of them.

. . There are: . combinations.

How many 3-letter combinations have 2 of one letter and 1 other letter?

There 3 choices for the pair (A, B, or C).

Then there are 3 choices for the single letter.

. . There are: . combinations.

Therefore, there are: . possible combinations.