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# how many combinations of three numbers can be found in any given quantity

Posted on 2013-02-04
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I have to work out and write down (on a spreadsheet):

how many groups of three numbers can be extracted (without repetition) from 80.

as an illustration:

there is only one group of three numbers in 3 (1,2,3)
there are four groups of three numbers in 4 (1,2,3  1,2,4  1,3,4  2,3,4)
there are 10 groups of three numbers in 6 (see attached worksheet)

I hope this calculation makes sense.

I need help with the formula for determining how many combinations, but in addition I also need them written out in a spreadsheet in an ordered way similar to that arranged in the attached worksheet.

I would be very grateful for help
sample-3.xls
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Question by:Europa MacDonald
• 5
• 3
• 3
• +1

Author Comment

ID: 38852272
I have =COMBIN(80, 3) for excel which gives me 18,424 possibilities

Now, what would be great would be a way of listing them all out in order.

1 2 3  (each number to its own cell)
1 2 4
1 2 5
1 2 6.... etc
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LVL 27

Expert Comment

ID: 38852277
For N numbers:  (N!) divided by (N-3)!*3!
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Author Comment

ID: 38852289
thankyou d-glitch, I have that already

I need some sort of code that will list them out, so that I can count the occurrence of combinations in a sample
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LVL 27

Expert Comment

ID: 38852299
No easy way to do that in Excel.  You need a programming language like AWK or Perl.
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LVL 44

Expert Comment

ID: 38852363
since there are 164,320 sets of 3 numbers in the result set, that will be quite a challenge to list each set in Excel.

AW
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Author Comment

ID: 38852382
Does Excel have a limit to the amount it can work with ?
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LVL 27

Expert Comment

ID: 38852410
If you have a programming language and an 80-element array,  you can do it with three nested loops:

For i = 1 to 80
For j = i to 80
For k = j to 80
Print   Array( i), Array( j), Array( k)
next k
next j
next i
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LVL 37

Expert Comment

ID: 38852412
Arthur, it's 3! not 3 in the denominator. So there's only 82,160 possibilities.
I don't see why Excel could not handle that. It might take a bit longer than other languages, but I can't imagine it running any longer than a minute. It could be done with either VBA (fairly simple) or formulas (a bit harder).

Does the assignment specify which you need to use?
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LVL 37

Expert Comment

ID: 38852426
Or since it's not an array and it's just numbers, you could just do.

``````row = 1;
For i = 1 to 78
For j = i+1 to 79
For k = j +1to 80
Range("A"&row).Value = i
Range("B"&row).Value = j
Range("C"&row).Value = k
row = row + 1
next k
next j
next i
``````
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LVL 27

Expert Comment

ID: 38852427
>> Does Excel have a limit to the amount it can work with ?

Yes.  64k rows and 256 columns.
That is plenty of space.  The problem is the available tools.
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LVL 27

Accepted Solution

d-glitch earned 2000 total points
ID: 38852433
Correction for the program ...

For i = 1 to 80
For j = i+1 to 80
For k = j+1 to 80
Print   Array( i), Array( j), Array( k)
next k
next j
next i
0

LVL 37

Expert Comment

ID: 38852441
64k is Excel 2003. The later ones will handle the 82160 just fine.
And lose the semicolon in the first line of my code
Also, combin(80,3) should give 82160 which is what I calculated earlier.
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