Define the unit N-hypercube to be the set of points [0,1]^{N} \subset \mathbb{R}^{N}. For example, the unit 0-hypercube is a point, and the unit 3-hypercube is the unit cube. Define a k-face of the unit N-hypercube to be a copy of the k-hypercube in the exterior of the N-hypercube. More formally, a k-face of the unit N-hypercube is a set of the form
\prod_{i=1}^{N} S_{i}
where S_{i} is either \{0\},\{1\}, or [0,1] for each 1 \leq i \leq N, and there are exactly k indices i such that S_{i}=[0,1].
The expected value of the dimension of a random face of the unit 8-hypercube (where the dimension of a face can be any value between 0 and N ) can be written in the form \frac{p}{q} where p and q are relatively prime positive integers. Find p+q.