In how many of the distinct permutations of the letters in "ABCCBCCBDDB" do the four B's not come together?

How many permutations of the letters ABCDEFGH contain the string ABC?

In how many of the distinct permutations of the letters in MISSISSIPPI do the four I's not come together?

How many ways are there to permute the 8 letters A, B, C, D, E, F, G, H so that A is not at the beginning and H is not at the end?

How many 3 letter words can you make from the letters A,B,C and D, where letters cannot be repeated and are in alphabetical order?

There are three English letters available: A, B, C and D. How many unique arrangements can Tom create using these letters?