Originally Posted by

**sapsapz** Hi there,

I have a question about combinatorics.

I came to understand that "n choose k" means that I have a pool of n objects, and I want to know in how many ways I could combine them. (Assuming the order doesnt matter, yellow and green is green and yellow).

So if the pool is Pool = {red, green, blue}, then all possible combinations of 2 of these objects would be 3. So far so good.

But then I read about Bernoulli trials, where if I have a coin of Head probability of p, and Tail probability of 1-p, then the probability to get exactly k times Heads out of n tosses, is (n choose k)*(p^k)(1-p)^(n-k).

So the expression (p^k)(1-p)^(n-k) is understood, it is the probability that a single valid "branch" on the tree of possible outcomes will be chosen, and the coefficient (n choose k) is supposed to give the amount of those valid branches.

I dont understand why n choose k is the way to arrive at this amount!

What is my "pool" here? It would seem that the order of the tosses is very important, we must consider the branch "Head Head Tail" and also the branch "Tail Head Head", etc, to add them up and get the correct probability.

I realize I'm mixing something up here, but I cant tell what it is.

Help, please?