[6439] in s-news-athena
COMBINATIONAL PROBLEM 15/2/95
daemon@ATHENA.MIT.EDU (Lotto Player )
Tue Feb 14 19:56:24 1995
To: s-news@utstat.toronto.edu
From: dwh@bom.gov.au (Lotto Player )
Date: Wed, 15 Feb 1995 00:13:49 GMT
COMBINATIONAL PROBLEM 15/2/95
Can anyone help ?
I have 3 sets of combinations sets a,b,c
Each set has the following numbers in it
For simplicity, I have numbered the set elements sequentially
set a 1,2
set b 3,4
set c 5,6
This gives one set d as 1,2,3,4,5,6 or 6 elements
I wish to calculate all combinations of the 3 sets
However, I wish to eliminate those combinations which have
elements which share the same set
I assume we would use select 3 from 6 as a starting point, producing 20 combinations.
However several of these combinations would have elements which share the same
set. Those combinations which have an x marked next to them have elements which share
the same set. There are 12 combinations having elements which share the same set. The
total of 20 combinations, less the 12 which share the same set gives us 8 unique combination
sets. This is what I wish to end up with.
My question is as follows.
Is there a formula which can be used to calculate the unique number of combinations
whose elements do NOT share the same set as shown in this example ???
And if so, cold you tell me what it is ?
Thanks
David
COMBINATIONS ( 3 from 6 = 20)
1,2,3 x
1,2,4 x
1,2,5 x
1,2,6 x
1,3,4 x
1,3,5
1,3,6
1,4,5
1,4,6
1,5,6 x
2,3,4 x
2,3,5
2,3,6
2,4,5
2,4,6
2,5,6 x
3,4,5 x
3,4,6 x
3,5,6 x
4,5,6 x
