I started to study statistical physics from a book, and it starts with basics about statistics and probabilities (which are things mostly new for me). In the book there is the following statement: "The simplest non-trivial system which we can investigate using probability theory is one for which there are only two possible outcomes. There would obviously be little point in investigating a one outcome system. Let us suppose that there are two possible outcomes to an observation made on some system S. Let us denote these outcomes 1 and 2, and let their probabilities of occurrence be P(1) = p, P(2) = q. It follows immediately from the normalization condition that p + q = 1, so q = 1 − p. The probability of obtaining n1 occurrences of the outcome 1 in N observations is given by PN(n1) = CN (n1,N−n1) p^(n1) q^(N−n1), (2.16) where CN (n1,N−n1) is the number of ways of arranging two distinct sets of n1 and N − n1 indistinguishable objects." I'm familiar with combinatorics, so I find it obvious that their CN (n1,N−n1) is Cn1 N. But I'm very curious how this can be proved. They give an example, but not a general demonstration. I've thought about it, but I couldn't do the demonstration. Can someone help me with it. I must mention: it is not homework, it is just for my personal knowledge.