A string of five letters is created using the letters $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$ and $\mathrm{E}$. How many of these letter strings are possible if:
a) No conditions are imposed
b) Repetition of the letter $\mathrm{A}$ is not allowed
c) Each letter string must begin with $\mathrm{C}$
d) $\quad$ B must be the middle letter
e) $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ must be the middle letters in any order with no repetition
For Part (e) please list all possibilities.