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

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 ( [tex]\frac{1}{6}\frac{}{}[/tex] )( [tex]\frac{5}{6}[/tex] )^{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