# Deriving the binomial distribution formula

1. Jun 10, 2010

I am trying to follow along with this derivation of the binomial distribution formula:
b(x;n,p) = nCx*pxqn-x

But I do not really understand the meaning of the part on bold. What is this "specified order" business now? I feel like I am missing something big here.

2. Jun 10, 2010

### Daft

Think about what the "nCx" part of the formula does.

Let's say we're rolling a regular dice 4 times, and we want the probability of a 6 only once. We know this would consist of 1 success and 3 failures ( $$\frac{1}{6}\frac{}{}$$ )( $$\frac{5}{6}$$ )3, however it does not account for which roll we get the 6, since it can occur in any 1 out of the 4 rolls, we multiply by 4C1.

So that "specific order" business is to eliminate the need to account for exactly when our successes occur

Does that make sense?