I'm trying to calculate the probability of winning powerball.
Using conditional probability without replacement I find that the chance of getting 5 white balls (69 uniquely labeled balls in total) correct is 1/1348621560. The problem is when I use binomial coefficients to find the number of possible coefficients I end up with a different probability of 1/11238513. Why do I get 2 different probabilities? I think I got confused somewhere can someone help?