# Keno Wheel

#### incyman

##### Member
Hello, I was wondering if anyone had a Keno wheel that would cover every 10 digit combination out of 20 numbers?

Does anyone know how many lines a wheel like this would be?

Thanks.

#### Beaker

##### Member
Go here and read that thread carefully I think the answer you are looking for might be there.

By my calculations there are 184,756 10 digit combos in 20 numbers.

corrected by Beaker - thanks for the clarification

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#### dwoods99

##### Member
I could be wrong, however I think the real number is 184,756 instead.
20! / (10! (20-10)!) = 20! / (10! * 10!)

Does that sound right to you ?

##### Member
Dwoods,

you got the nrs right but the name's wrong , beaker doesn't have pointy ears and whiskers...at least his avatar doesn't

Cheers

for the guests not up on factorials (!) another way to calc all the combos is: 20x19x...x12x11/(10x9x...x3x2)

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#### dwoods99

##### Member

Another lesson for factorials which I use is to cross out numbers... so (20! / (10! * 10!) gives

Note: I am using '.' to mean multiplication.
20.19.18.17.16.15.14.13.12.11.(10!)
----------------------------------------------- =
10.09.08.07.06.05.04.03.02.01.(10!)

Cross out 10! on top and bottom, cross out 20 on top and (4.5) on bottom, cross out 18 on top and (3.6) on bottom, cross out 14 on top and (2.7) on bottom, cross out 1 on bottom because 1 is 1. This leaves...

19.17.16.15.13.12.11
-----------------------------
10.09.08 (which is 720)

so now it's easy to grab a calculator to get the answer.

As an exercise calculate the following,
the 6/49 odds of winning are (49! / (6! * (49-6)!)) = 13,983,816,
and Super 7 is (47! / (7! * (47-7)!)) = 62,891,499.

Lesson concluded for today