list of all keno combinations for 6 numbers?

You're forgetting that because 20 numbers are drawn, even if a player hits a 6/6 there are 14 numbers the player didn't match, and the presence of all those extra numbers increases the player's odds of hitting the 6/6.

The effect of this on the mathematics is that there are many different 6-number combinations that will hit a 6/6 for any given draw of 20 numbers, so there are many more 6-number combinations than you figured, even if we eliminate variations in the order as a consideration. (Eliminating variations in order is quite standard in this sort of math; in fact, we generally define a "combinations" as calculated that way. See the link below in source for the basic mathematics of order-independent combinations, in relation to "permutations" which is the term for order-sensitive variations.)

There are in fact

C(80,6) = 80! / (74! 6!)

= 80 * 79 * 78 * 77 * 76 * 75 / (6 * 5 * 4 * 3 * 2 * 1)

= 2 * 79 * 13 * 77 * 76 * 25

= 300,500,200 different 6-number combinations, far too many to list here.

(Answers does impose length limits.)

Each 20-number draw will produce 6/6 matches on

C(20,6) = 20! / (14! 6!)

= 20 * 19 * 18 * 17 * 16 * 15 / (6 * 5 * 4 * 3 * 2 * 1)

= 19 * 17 * 8 * 15

= 38,760 different 6-number combinations.

The odds of hitting a 6/6 are derived from both these numbers:

(300,500,200 - 38,760) to 38,760

= 300,461,440 to 38,760

= about 7,751.8 to 1

The figure you had, 7,752.8 to 1, was not actually odds but the basis of the probability calculation, correctly expressed as approximately 1/7,752.8

Nora Laverne: 6/10. i appreciate Nora yet i'm unlike Laverne. i ought to elect to slide Vivienne contained in the middle call slot, then it will be a 10! Claire Henrietta: 6/10. lovable. Elena Vivienne: 4/10. i ought to like it better if it were Elena Laverne. :)