Classical Probability Model

Hi, well I'm totally lost with this subject, and this is an easy question but I just don't understand ..

Question: A fair coint is flipped n = 100 times. What is the probability to have exactly k = 50 heads? What is the probability to have exactly n/2 heads when n is even?

Answer:

Use the Classical Probability Model: $\displaystyle P(E) = \frac{N(E)}{N(S)}$ with $\displaystyle N(S) = 2^{100} $

*<I don't understand why it is *$\displaystyle 2^{100}$*. Why isn't it just 100? >*

So $\displaystyle P(E) = \frac{100!}{50!50!} \times 2^{-100}$

*<Again, I don't get why we're using the combination formula? Why isn't it just *$\displaystyle \frac{50}{100}$*...????>*

*Can someone please explain this to me?*