How to Figure Odds of Holding a Winning Lottery Ticket

Some folks are under the impression that the odds of winning a multi-state "Powerball" lottery are even slimmer because so many people play it. But actually the odds of winning have nothing to do with how many people play and everything to do with how many numbers can be picked. A simple math combination formula can tell you how lucky you will have to be to win.

Instructions

1. Know the formula for a math combination: [(n! / (n - r)!*r!)]. The "n" is the number of balls in the lottery, the "r" is the number of balls chosen for each drawing and "!" represents the factorial in the formula.

2. Determine "n," the number of balls that numbers can be chosen from. If you can choose a number from 1 to 55 for your lottery, 55 is "n." In Powerball, you also have to match the red ball from 1 of 42 numbers. You will need to plug in numbers for this combination separately in the same formula.

3. Set your "r," the number of numbers (or balls) chosen for each drawing. If your lottery picks 5 balls, then your "r" is 5.

4. Plug your "n" and "r" into the formula. For the above example, your formula would look like this: [55!/(55-5)!*5!].

5. Simplify the formula to find your odds of holding the winning lottery ticket. Although the factorial looks cumbersome, most of the work is easily simplified by reducing the top of the fraction by the bottom of the fraction. The formula becomes: (55*54*53*52*51) which equals: 417451320 divided by 120 (which is 5).

6. Grasp that your odds of matching all five balls are 1 in 3,478,761. To match the one red ball in Powerball, your odds are in 1 in 42. Multiply that number by the odds of matching all 5 white balls and you have your odds for winning the whole thing: 1 in 146,107,962.00.