Powerball is a lottery in which most U.S. states participate. To play, you pay $2 and choose five white numbers between 1 and 59. Then you choose a single red ball, the Powerball, from a second set of numbers that range from 1 to 35. To win the Powerball jackpot, you must match all five white numbers, plus the Powerball number. Like other lottery games, varying amounts of money can also be won by matching fewer numbers, allowing for nine different ways to win a Powerball prize. Here are the different ways.
• 5 white + Powerball = Powerball jackpot prize, $40 million minimum (Probability of winning: 1 in 175 million)
• 5 white = $1 million prize (Probability of winning: 1 in 5.2 million)
• 4 white + Powerball = $10,000 prize (Probability of winning: 1 in 650,000)
• 4 white = $100 prize (Probability of winning: 1 in 19,000)
• 3 white + Powerball = $100 prize (Probability of winning: 1 in 12,000)
• 3 white = $7 prize (Probability of winning: 1 in 360)
• 2 white + Powerball = $7 prize (Probability of winning: 1 in 706)
• 1 white + Powerball = $4 prize (Probability of winning: 1 in 111)
• Powerball only = $4 prize (Probability of winning: 1 in 55)
The Powerball jackpot starts at $40 million and increases after each drawing with no Powerball jackpot hit. The largest Powerball jackpot on record (as of 2014) is $590.5 million, won in May 2013, by a ticket sold in Florida.
How many possible combinations of six Powerball numbers are there, where five white numbers are chosen from 1 through 59 and one red Powerball number is chosen from 1 through 35?
The rules that you have stated in your question have been changed since 2015 and are no longer used. Read about the new rules and the odds here in Wikipedia:
https://en.wikipedia.org/wiki/Powerball
How many possible combinations of six Powerball numbers are there, where five white numbers are chosen from 1 through 59 and one red Powerball number is chosen from 1 through 35?
The above odds that you want calculated are obsolete. But even so, the old odds were:
59C5 x 35 =175,223,510 to 1
The new odds are:
69C5 x 26 =292,201,338 to 1
This is how you figure that out:
[59 x 58 x 57 x 56 x 55 x ............all the way down to 1] / [54 x 53 x 52 x 51......all the down to 1 x [5 x 4 x 3 x 2 x 1] =[59 x 58 x 57 x 56 x 55] /[5 x 4 x 3 x 2 x 1] =600,766,320 / 120 =5,006,386. Then you would multiply this number by 35 =175,223,510
