Powerball odds and oddities
I was having a discussion recently trying to make someone understand why buying $5 worth of Powerball tickets does not dramatically improve your chances of winning. The formula for number of possible combinations is usually listed like this, when we choose “n” items out of “m” possible items.
C(m,n) = m! / ((n!)*(m-n!))
In the case of the powerball, we have 55 white balls, taken 5 at a time or: 55! / (5!)*(50!) where ! denotes a factorial.
Doing some simple algebra, we effectively have (55*54*53*52*51)/(5*4*3*2*1) which gives us 3,478,761 possible combinations without taking into account the PowerBall number. In order to take the powerball number into account, we have to multiply this number by 42 (since there are 42 unique powerball numbers and we always choose one of them), which gives us 146,107,962 different possible winners.
How does spending $5 instead of $1 improve your chances of winning? Not much. With $1, we have one of the 146,107,962 possible combinations. With 5$, we have a 5 of 146,107,962 of possible numbers (assuming we spend our $5 on unique combinations). In other words, there are 146,107,957 other possible winners for a given drawing. Are you feeling lucky?
May 27th, 2006 at 10:13 pm
How can there be that many combinations, it doesnt seem possible. Out of the five balls of 55, i can only come up with like 27,000 or so. I am not a math genious but I have wasted alot of time with this. one by one i have listed possible combinations, and still I cant get as many as you. please help.