Understanding Binomial Coefficients: Solving a Sample Problem

[Hessinger]

I understand permutations, combinations and such, but I can't seem to make sense of binomial coefficients, or at least the notation.

As an example, could someone walk me through the notation for a generic problem.. something like 100 people eligible for an award and the winner can choose 1 prize among 5 choices.

 

[SW VandeCarr]

Note $$(x+y)^n=\sum_{k=0}^{n}\left(\begin{array}{cc}n\\k\end{array}\right) x^{n-k}y^{k}$$ or you can use Pascal's Triangle to get the binomial coefficients.

 

[JSuarez]

What is precisely that you don't understand about binomial coefficients? You say that you understand combinations, but the binomial coefficients are numerically equal to combinations without repetition, so please be more specific about your problem.