Homework Help: Deriving the binomial distribution formula

1. Jun 10, 2010

Saladsamurai

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?

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook