well i used counting techniques for 2) _ _ _ _ _ _ _ and if e always precedes i, so theres 6 ways that can be done, and theres 5 slots left, so 5 factorial. .. :S
E I _ _ _ _ _
_ E I _ _ _ _
_ _ E I _ _ _
_ _ _ E I _ _
_ _ _ _ E I _
_ _ _ _ _ E I
and then 5 spaces for the other letters so 5...