Re: Great Article on Buying All Powerball Numbers
Posted by:
Hmmm...
()
Date: January 08, 2016 11:38AM
That was true for the old 59/35 game. But the basic game changed back in October. There are now 69 white balls in the regular ball drum and 26 red balls in the powerball drum. This means that there are actually 292,201,338 possible outcomes for each drawing. A $2 ticket for each one of those would cost you $584,402,676.
Here are the calculations for those who have had limited or no exposure to the notion of permutations and combinations. Since there are 69 balls in the regular drum, there are 69 possible outcomes for the first ball drawn. That ball is NOT put back into the drum however, so for the second ball drawn there are only 68 possible outcomes remaining. In the same way, there are just 67 possible outcomes for the third ball, 66 for the fourth ball, and 65 for the fifth ball. The total number of possible outcomes then is 69 times 68 times 67 times 66 times 65. That's a total of 1,348,621,560. But there's a problem. The outcomes 1-2-3-4-5 and 5-4-3-2-1 would be considered as different outcomes at this point when for prize-winning purposes, they are the same. You can remove the problem by dividing the first total by what is known as 5-factorial. That's 5 times 4 times 3 times 2 times 1, or 120. That would leave you with 11,238,513 possible outcomes, but you still have to pick the powerball, so you need to muliply by 26. That gives you the final total of 292,201,338 possible outcomes as shown above.