4
In addition to Lord_Farin's options, I'll include one-and-a-half using multline (which he apparently does not favour).
$$P(E) = \dfrac{\begin{multline}\text{ 1 choice for C1 } \times ... \times \text{ 1 choice for C(k - 1) } \times \text{ 1 choice for C(k) } \\ \color{red}{\times N} - k \text{ c...