Powerball odds question.

Factual Questions
1

I think I am doing the math all wrong on this, but it is my understanding that the odds are the total number of combinations to 1 correct?

According to the powerball web site the odds are ~120,526,770

However, when I do my math on my computers caculator (since my handheld just goes funky on me at that high of numbers), I get 16,185,023,400!!

That is assuming these things- 53 white balls are drawn out of the lot- Since there is only one copy of each number, each consecutive draw has 1 less maximum chance. So I did this caculation- 53 X 52 X 51 X 50 X 49 X (47) <- number of RED balls.

How come the web site has such low odds in comparison to what I got? Am I not understanding some basic principle of odds or what? I double and triple checked my answer, so that isn’t it…

2

Your calculations would be correct if the order the numbers were drawn mattered, which doesn’t in powerball. The numbers 1 2 3 4 5 are the same as 3 1 5 2 4 and the same as all the other 118 combinations those 5 number make up. The correct way to figure it is to start as you did by multiplying 53x52x51x50x49. This is 344,362,200. Then divide this by 5x4x3x2x1 which is 120, the number of combinations any set of 5 things has. (This is the step you left out.) Now you have 2,869,685. Then you multiply this by 42 (this, not 47, is the number of red balls) and you will get 120,526,770.

3

Aha!

Thanks. Makes sense now.