Question

. The lottery has determined that not enough people win so they are making it easier by having players pick from fewer numbers. As with all “pick numbers” lotteries, there are full winners and partial winners. To be a full winner, you need to pick 6 main numbers correctly out of 24, and you also have to pick one bonus number out of an additional 4. What are the odds of winning (i.e. 1 chance in XXXXX) for all of the following winning combinations?

Answer 1

Number of ways to select r items from n, nCr = n!/(r! x (n-r)!)

Number of ways to pick 6 main numbers out of 24 = 24C6

= 134,596

Number of ways to pick bonus number = 4

Total number of tickets possible = 134,596 x 4

= 538,384

Number of winning tickets = 1

Number of losing tickets = 538,384 - 1 = 538,383

Odds of winning = 1 in 538,383