After each coin flip, I record a H for heads and T for tails. Flipping the coin n times, I will get a sequence of letters like this: HHTHTTTH... with n letters in it. The probability that I get k heads in a row followed by n-k tails in a row is . What if I get k-1 heads, then a tails then a heads, then the rest are all tails is the same probability. In fact, any sequence of k H's and (n-k) T's corresponds to a sequence that results in exactly k heads flipped. It is not possible the have two different orders occur simultaneously, so they are disjoint cases. We just count the number of ways to order the k H's and (n-k) T's. Then, we multiply by the probability of getting k heads and (n-k) tails in a specific order. So, we have n positions and we choose k of them to be heads. Now we don't have any choices left. The remaining n-k positions must be tails.