According to Powerball.com, the game is played like this
…we draw five white balls out of a drum with 69 balls and one red ball out of a drum with 26 red balls
Their odds explain that the change of you winning the jacketpot and matching the first five numbers plus the red ball are: 1 in 292,201,338. Why?
Why wouldn't it be (69*68*67*66*65)*26 = 1 in 35,064,160,560?
I have seen online some people use the COMBIN function in Excel to calculate this but it doesn't make sense to me?
Thank you!
Best Answer
Probably the order of the five white balls does not matter, so you have to divide by $5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ to account for the different orders in which these could be drawn.
Your calculation would be correct if the order did matter, i.e. if 1,2,3,4,5,6 wins, but not 2,1,3,4,5,6.