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Number of odd combinations in a 5/39 game

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There are a total of 575,757 combinations of 5 numbers in a 5/39 game.

Since there are 19 even numbers in the set of 39 numbers, and 20 odd numbers, it seems to me that there are a slightly larger number of combinations with a 3 odd 2 even split, than a 3 even 2 odd split.

Does any one know how to calculate the number of 3 odd 2 even combinations? If so, how many are there?  Thanks in advance.

johnph77's avatar - avatar

You are correct.

 

The number of combinations in 3/20 can be calculated with the formula (20x19x18)/1x2x3) = 1,140.

The number of combinations in 2/19 can be calculated with the formula (19x18)/(1x2) = 171.

Multiplying these two results will give you the total number of 3 odd/2 even in a 5/39 game - 194,940.

Conversely, the number of combinations in 3/19 can be calculated with the formula (19x18x17)/(1x2x3) = 969

The number of combinations in 2/20 can be calculated with the formula (20x19)/(1/2) = 190.

Multiplying these two results will give you the number of 2 odd/3 even in a 5/39 game - 184,110.

GiveFive's avatar - Lottery-026.jpg
In response to johnph77

Thanks so much!

Coin Toss's avatar - shape barbed.jpg

GiveFive

"Perimeter" numbers ( top sand bottom row, left and right outside columns) work out the same way, 20 and 19, but it just doesn't seem to matter as far as predictability goes. Not drawing by drawing. If you were to play thousands of drawings, sure, it would prove itself out, but day by day, goos luck.

GiveFive's avatar - Lottery-026.jpg
In response to johnph77

If I want to calculate the number of combinations in a "group" of numbers in a 5/39 game, how would I do that?  For instance, if I take the entire set of 39 numbers (1 - 39) and break it into 3 ranges of numbers. 

(1 - 13, 14 - 26, & 27 - 39)

How many possible combinations of 5 numbers are there in each of those three ranges?   Thanks again!

johnph77's avatar - avatar

Each group you cite has 13 numbers. The formula for 5-number groupings from 13 possibilities would be: (13x12x11x10x9x8)/(1x2x3x4x5) - 1,287.

GiveFive's avatar - Lottery-026.jpg
In response to johnph77

Once again, thank you very much!

I'm curious as to why you stopped multiplying after using 8 in thr front half of the equation.  Since there are 5 numbers picked, why wouldnt you stop after using 9?  If it's too complicated or complex to easily explain in a post, then that's fine....  I'm simply curious and I dont have a burning need to know!

BTW, prior to posting here, I Googled "calculating lottery odds", and I got quite a few hits.  Some sites even have built-in calculators that will do the math for you, but I didnt see exactly what I was looking for.

johnph77's avatar - avatar

Because I screwed up. When entering the formula, "8" shouldn't be included - there are only five numbers in the desired combination.

The correct formula (and the one I used to obtain the actual number of combinations) is: (13x12x11x10x9)/(1x2x3x4x5) - 1,287

GiveFive's avatar - Lottery-026.jpg
In response to johnph77

After I submitted my post, I used a calculator and did the math w/o using the 8, and got a result of 1,287!  Had I done that first, then I wouldnt have needed to bother you!  Sorry!

E-mailed you a link to the website.... Thanks!

johnph77's avatar - avatar

Thanks for pointing out my error and giving me the chance to correct it.

B$Rizzle's avatar - a4leds
In response to johnph77

Another way to calculate the different possiblities in a group of numbers is by using the COMBIN function in excel

 

For example say you have 15 numbers you play and you want groups of 3. The function would be :

=COMBIN(15,3)

 

that would give you 455 combinations.

 

Not sure if that helps or not but its pretty cool

GiveFive's avatar - Lottery-026.jpg
In response to B$Rizzle

Thanks for the tip!  I'll give it a try.

And you're right, it is cool!

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In response to johnph77

Is there a way to get EXCEL to 'create' the list of 1287?

winsumloosesum's avatar - Lottery-060.jpg

Below is a download link to an Excel file that will generate 1287 combinations per group.

http://www.box.net/shared/0p4mx5hohn

Open the Excel file and in cell C1 enter either a 1, 2, or 3. 

Click an empty cell under cell C1. 

Then click the Toolbar.

The 1287 combinations will appear starting in cell M1.

In cell H1 you will see the legend for each Group number.

GiveFive's avatar - Lottery-026.jpg
In response to winsumloosesum

Winsum,

Very nice spreadsheet, thanks!

Something has been bothering me about the possible number of 5 number combos in a group of 13.  I printed out a chart  from a website that shows many many more combo's for a group of 12.  (1 - 12, 13 - 24, & 25 - 36) 

I agree that the forumla johnph77 provided is correct, so how the people that generated the chart that appears on that website actually generated the numbers for their chart is a mystery to me.

You can see the chart at <snip> dot com slash ruletwo dot htm. 

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