Another way to write this is the number of ways, given that you have n buckets, you can put k things in them without having to differentiate it. Another way to think about it is if you have n buckets or n flips and you want to choose k of them to be heads, or you want to choose k of them in some way but you don't want to differentiate. All of these are generalized ways for binomial coefficients. Going back to the original problem, what is the probability of getting k heads in n flips of the fair coin? There's 2 to the n equally likely possibilities. Let's write this down. The probability of 2 to the n equally likely possibilities, and how many of those possibilities result in exactly k heads?