Suppose we have 3 A's, 5 B's, 7 C's, 9 D's, and one E, F, G, and H.

1. How many different arrangements of these letters are possible if I write them as a string?

I believe this is 28! / (3! 5! 7! 9!). Seems pretty simple.

2. If I write my "string" as a loop, either around in a circle or around the outside of a cylinder(so there is not just one beginning or end), how many different arrangements are possible?

My attempt...

For each permutation; there are 27 others that are considered to be identical?

[28! / (3! 5! 7! 9!)] / 27.