In mixing ethanol and water is the tendency toward randomness, one that favours ethanol and water being mixed or being separated in solution?

I don't know what you are asking here, but let me tell you this:

Polar molecules dissolve in polar solvents only
Non-polar molecules dissolve in non-polar solvents only

The OH group in water and in ethanol is polar, hence, one will dissolve in the other.

However, the CH3 group is not polar and will have a tendency to separate the two. But since the polarity of the OH group is predominant here, ethanol dissolves in water.

As the alkyl group becomes longer, it's ability to separate the alcohol from water increases. Butanol is immiscible with water, and so are the longer alcohols.