In my discrete math book we keep coming back to using a coin flip. When doing random variables and expected value they use the coin flip again to figure out how many heads on 3 coin flips. However, they do it by hand listing out each iteration to find the number of heads.
As an example if a coin is flipped 3 times and you want to know the number of permutations have 2 heads. In the book they do
X(HHT) = X(HTH) = X(THH) = 2 X(TTH) = X(THT) = X(HTT) = 1
That makes a lot of sense. However I am being presented a problem that is a coin is flipped 8 times. I really don't want to write down 256 variations just to the random variable of H.
So my question is. Is there a way to find this out mathematically? I swear I have to be missing something while looking up how to do it.