\\
works:
$$P(E) = \dfrac{\text{ 1 choice for C1 } \times ... \times \text{ 1 choice for C(k - 1) } \times \text{ 1 choice for C(k) }\\\color{red}{\times N} - k \text{ choices for C(N - k) }\times N - k - 1 \text{ choices for C(N - k - 1)} \times ...}{N!}$$
$$P(E) = \dfrac{\text{ 1 choice for C1 } \times ... \times \text{ 1 choice for C(k - 1) } \times \text{ 1 choice for C(k) }\\\color{red}{\times N} - k \text{ choices for C(N - k) }\times N - k - 1 \text{ choices for C(N - k - 1)} \times ...}{N!}$$
Double line (using the non-breaking space character ~
):
$$P(E) = \dfrac{\text{ 1 choice for C1 } \times ... \times \text{ 1 choice for C(k - 1) } \times \text{ 1 choice for C(k) }\\~\\\color{red}{\times N} - k \text{ choices for C(N - k) }\times N - k - 1 \text{ choices for C(N - k - 1)} \times ...}{N!}$$
$$P(E) = \dfrac{\text{ 1 choice for C1 } \times ... \times \text{ 1 choice for C(k - 1) } \times \text{ 1 choice for C(k) }\\~\\\color{red}{\times N} - k \text{ choices for C(N - k) }\times N - k - 1 \text{ choices for C(N - k - 1)} \times ...}{N!}$$
Or use the align
environment:
$$P(E) = \dfrac{\begin{align}&\text{ 1 choice for C1 } \times ... \times \text{ 1 choice for C(k - 1) } \times \text{ 1 choice for C(k) } \\ &\color{red}{\times N} - k \text{ choices for C(N - k) }\times N - k - 1 \text{ choices for C(N - k - 1)} \times ...\end{align}}{N!}$$
$$P(E) = \dfrac{\begin{align}&\text{ 1 choice for C1 } \times ... \times \text{ 1 choice for C(k - 1) } \times \text{ 1 choice for C(k) } \\ &\color{red}{\times N} - k \text{ choices for C(N - k) }\times N - k - 1 \text{ choices for C(N - k - 1)} \times ...\end{align}}{N!}$$
$$P(E) = \dfrac{\begin{align}&\text{ 1 choice for C1 } \times ... \times \text{ 1 choice for C(k - 1) } \times \text{ 1 choice for C(k) } \\ \\&\color{red}{\times N} - k \text{ choices for C(N - k) }\times N - k - 1 \text{ choices for C(N - k - 1)} \times ...\end{align}}{N!}$$
$$P(E) = \dfrac{\begin{align}&\text{ 1 choice for C1 } \times ... \times \text{ 1 choice for C(k - 1) } \times \text{ 1 choice for C(k) } \\ \\&\color{red}{\times N} - k \text{ choices for C(N - k) }\times N - k - 1 \text{ choices for C(N - k - 1)} \times ...\end{align}}{N!}$$