Say I have 8 balls, 4 of which are green and 4 are red. I want to calculate the probability of getting 4 green balls. When I use this formula :

4c4 / 8c4

I arrive at the correct result - 1/70 around 0.14

However, when I use the direct binomial distribution :

(n/k)*p^k*(1-p)^(n-k)

Where,

p=0.5 (8/4)

n=8

k=4

I arrive at a value of around 0.2...

If someone could tell me where i'm going wrong it would be really helpful. Thanks in advance.