# Probability of winning Powerball Lottery?

#### poisonroxs

##### New member
I have done this problem, however I do not feel confident in my answer, can anyone confirm if it is correct?

$1 lottery ticket Lottery draws 5 out of 55 white balls (1 of 55 inclusive) and 1 out of 42 for the powerball (1 of 42 inclusive) How much would you have to spend to play all of the possible winning combinations to be sure you would win? nCr n=55 r=5 n!/r! (n-r)! 55!/5! (50)! (5!)^2 (50!)^2/(5! 55! (45+5)! (5-5)!^2 *1/42 55 X 54 X 53 X 52 X 51/5 X 4 X 3 X 2 X 1 120/55 x 54 x 53 x 52 x 51x 42 = 1 out of 146,107,962 chance of winning with buying 1 ticket so you would have to spend$146,107,962 to play all possibilities, which is stupid because no lottery prize is that high.

Any feedback would be greatly appreciated

#### galactus

##### Super Moderator
Staff member
No lottery is that high?. I beg to differ. What about the \$300, 000,000 mega-million?. It often goes higher than 146 million.

As for the possible combinations:

You must choose 5 out of 55, C(55,5)=3,478,761

Then you have to choose 1 out of 42, C(42,1)=42

Then you get (3,478,761)(42)=146,107,962 possible combinations.

And you are correct.

#### poisonroxs

##### New member
Wow, I had no idea that jackpots went that high. So if you had 150 million to invest and the time to actually play all of the possible outcomes, you could double your money? Even after paying taxes that would still be worth it, right?
Thank you so very much for confirming that the answer I had was correct )

#### daon

##### Senior Member
poisonroxs said:
Wow, I had no idea that jackpots went that high. So if you had 150 million to invest and the time to actually play all of the possible outcomes, you could double your money? Even after paying taxes that would still be worth it, right?
Thank you so very much for confirming that the answer I had was correct )
Keep in mind there are about 32 million seconds in a year. With that enormous staff you'd have to hire just to buy your tickets, you might just break even. :wink:. Oh yeah... then there's finding the ticket assuming one of your staff haven't run off with it. (thats only assuming the lottery is once a year... most lotteries are at least once a week).