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If the powerball is drawn from the same pool of numbers as the main lottery, then, for a given target score, the number of winning combinations includes the powerball.
This can be written in a general form for all lotteries as: ( K B ) ( N K K B ) ( N K ) displaystyle K choose BN-K choose K-B over N choose K where N displaystyle N is the number of balls.The odds are dependent on the total number of tickets that are played.This yields a final formula of ( n k ) ( 49 6 ) displaystyle n choose k49 choose 649 over 6*48 over 5*47 over 4*46 over 3*45 over 2*44 over 1 The range of possible combinations for a given lottery can be referred.It is based heavily grand casino kursaal bern on combinatorics, particularly the twelvefold way and combinations without replacement.The look and functionality of our online free wheels are NOT the same as our Wheel Six Gold software, though the formulas that produce the wheels are the same as they are in the software.If you're behind a web filter, please make sure that the domains *.kastatic.Simply click on 18 boxes next to the 18 lotto numbers you want to wheel (only choose numbers that are in your game's number field Simply type the 18 numbers you want to wheel in the lettered boxes, then click on Generate Combinations.For example, in the 6 from 49 lottery, given 10 powerball numbers, then the odds of getting a score of 3 and the powerball would be 1.66 10, or 566.6 (the probability would be divided by 10, to give an exact value.Gail Howard recommends wheeling less than about half the numbers in your game, so you do not need to look for a wheel that includes as many numbers as your game.Using the same principle, the odds of getting a score of 2 and the powerball are ( 6 2 ) ( 43 4 ) 1, 851, 150 textstyle 6 choose 243 choose 41,!851,!150 for the score of 2 multiplied by the probability of one.Use Smart Luck's Interactive 30-Second Lotto Wheel 608 free.The total number of combinations giving that result is, as stated above, the first number multiplied by the second.Get the Software that Contains this Wheel and More!For games based on the Canadian lottery (such as the lottery of the United Kingdom after the 6 main balls are drawn, an extra ball is drawn from the same pool of balls, and this becomes the powerball (or "bonus ball.The expression is therefore ( 6 n ) ( 43 6 n ) ( 49 6 ) displaystyle 6 choose n43 choose 6-n over 49 choose.Of the 258 combinations that match 5 of the main 6 balls, in 42/43 of them the remaining number will not match the powerball, giving odds of ( 49 6 ) 3 166, 474.In the 5-from-90 lotto, the minimum number of tickets that can guarantee a ticket with at least 2 matches is 100.

In particular, the information content of outcome x displaystyle x of discrete random variable X displaystyle X is I X ( x ) : log p X ( x ) log ( 1 p X ( x ) ).