Say you have two black balls and two white in a jar and you pick 3 at random. When one is picked it is taken out of the jar. I want to know the probability of getting for instance WWB. That must be: P(WWB) = 1/2*1/3*1 = 1/6 Now say you want WBW. Then you get: P(WBW) = 1/2 * 2/3 * 1/2 = 1/6 Amazingly enough the probabilities are independent on the order in which you choose your balls. This result is kind of amazing for me and not really intuitive. So far it stands more or less as a defining property of this kind of combinatorics. Is it intuitive for you that the order really is independent? What argument would you give for this? And lastly, perhaps even more interestingly: Can anyone prove that if you general have NA blue elements and NB red elements then the number of ways of getting a blue and b red elements is independent of order. I don't know if it's an established theorem - if so, where can I read more about it?