The audio segment ends with Charlie McDonnell (of the British "Fun Science" videos) noting that "every now and then, at random, you end up with something awesome." We might take that to mean that every now and then, a simple random sample is representative of a population with respect to a certain list of demographics. Let's look at a simple example to see how likely that might be. Suppose you have a population with two men-one a Republican and one a Democrat; and two women-one a Republican and one a Democrat. 

1. List all possible distinct samples of your notation makes it possible to size two from this four-person population. Make sure that distinguish all four members of the population. 
2. For a simple random sample of size two, all samples of size two have the same chance of being chosen. What would the likelihood be of choosing any one of these samples? 
3. Suppose for a sample of size two to be "representative" of the population, it has to have exactly one man and one woman, and one Democrat and one Republican. What is the chance of selecting a simple random sample of size two from this population that is representative (in this series of the word)?