Please explain each question step by step

1. [T, 4 points] How many permutations of all the letters {A.B.C.D,E.F.G} a) Contain the string 800? b) Contain the strings BA and GF? c) Contain IetterA or letter C in the middle? d) Contain the letters F and B next to each other? E) the arrangements doesn't contain the letter F and B next to each other