8 0 13.8563731865619

8 1 4.15691195596856

8 2 3.06298775702947

8 3 4.25414966254092

8 4 10.2099591900982

8 5 41.477959209774

8 6 293.11091174907

8 7 3956.99730861244

8 8 133929.139676113

Keno 75/20 Spot=: 8 (Same as 75 Bingo numbers, 20 drawn, must match 8: the last number is what you're looking for)

from this calculator site, where you can plug in the numbers you're wondering about (8 numbers called, 9, 10, etc...from your post above).

There are (75)C(20) = 803,167,998,494,073,240 ways to draw 20 numbers out of 75.

Color the balls of your eight chosen numbers red, and the other 67 numbers white.

For 8 out of 8, the 20 balls drawn are 8 red and 12 white.

There is (8)C(8) = 1 way to draw 8 red balls out of 8, and (67)C(12) = 5,996,962,277,488 ways to draw 12 white balls out of 67.

The probability of 8 out of 8 = (1 x 5,996,962,277,488) / 803,167,998,494,073,240 = 1 / 133929.139676113.

For 7 out of 8, the 20 balls drawn are 7 red and 13 white.

There are (8)C(7) = 8 ways to draw 7 red balls out of 8, and (67)C(13) = 25,371,763,481,680 ways to draw 13 white balls out of 67.

The probability of 7 out of 8 = (8 x 25,371,763,481,680) / 803,167,998,494,073,240 = 1 / 3956.99730861244.

Quote:ThatDonGuyAnd here's how the numbers are calculated:

There are (75)C(20) = 803,167,998,494,073,240 ways to draw 20 numbers out of 75.

Color the balls of your eight chosen numbers red, and the other 67 numbers white.

For 8 out of 8, the 20 balls drawn are 8 red and 12 white.

There is (8)C(8) = 1 way to draw 8 red balls out of 8, and (67)C(12) = 5,996,962,277,488 ways to draw 12 white balls out of 67.

The probability of 8 out of 8 = (1 x 5,996,962,277,488) / 803,167,998,494,073,240 = 1 / 133929.139676113.

For 7 out of 8, the 20 balls drawn are 7 red and 13 white.

There are (8)C(7) = 8 ways to draw 7 red balls out of 8, and (67)C(13) = 25,371,763,481,680 ways to draw 13 white balls out of 67.

The probability of 7 out of 8 = (8 x 25,371,763,481,680) / 803,167,998,494,073,240 = 1 / 3956.99730861244.

Thanks, TDG! Wasn't sure anyone else was going to answer, so I directed him to a calc. Much prefer that you proofed it out.

Quote:jbeck2862I am currently looking into what the minimum number of sets I would need to play in order to guarantee a win at 20 numbers even though the number would be to great to be physically possible. I am just curious to know what that number actually is. I also think that if I could come up with said set and played from it I would have better odds but that is probably just wishful thinking.

This sort of problem is well-known, and while an "exact" formula still escapes mathematicians, somebody came across a lower bound for the value; in this case, you need at least 275,737 tickets for at least one 8-number hit and 64,966 tickets for at least one 7-number hit.

The lower bound (i.e. the actual number >= this) for a draw of p numbers out of n where each ticket has k numbers and you want to match at least t on at least one ticket is:

combin(n,k) x (n - p + 1) / (combin(p-1, t-1) * combin(k, t) * (n - t + 1))

In this case, n = 75, p = 20, k = 8, and t = 7 or 8 as appropriate.

See theorem 1.16 here

http://www.jsonline.com/news/milwaukee/112642749.html