question in permutation and combination

1.list all permutation for the letter a, c, t

2. a) how many permutations are there for the eight letters a, c, f, g, i, t, w, x ?

     b) consider the permutation in part(a). How many start with the lettert? how many start with the letter t and end   with the letter c?

3. Evaluate each of the following

     a)P(7,2)

     b) P(8,2)

4. in how many ways can the symbols a, b, c, d, e, e, e, e, e be arranged so that no e is adjacent to each other?

5. a) P(n,2)=90

    b) P(n,3)=3P(n,2)