Hi Tutors!

I need some help with Discrete and Combinatorial Mathematics questions. I have already attempted and completed each of these, but I would like to see how experts approach each question since I may not be doing these questions the "efficient" way. Thank you!

1) List all strings of size 3 over the alphabet {A, B}.

2) Find all permutations of {X, Y, Z}

3) Find all strings of length 4 over the alphabet {0, 1, 2} with the property that there are no 10, 21, 20 substrings.

4) Find all 8 graphs with the vertex set V = {1, 2, 3}.

5) Find all graphs with the vertex set V = {1, 2, 3, 4} that are cycles.

6) Draw a rooted tree with 9 vertices and no vertex of level 3.