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July 24th, 2009, 11:17 AM   #1
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Determining the number of combinations for n paired events

Hi All,

I'm trying to come up with a formula that will calculate the possible combinations of a set of paired events.

To give an example:
There are 6 events, A1, A2, B1, B2, C1, C2
A2 can not occur unless A1 has occured, but A2 does not necessarily need to occur immediately after A1, similarly for B1/B2 and C1/C2
A1 B1 and C1 can occur in any order
All 6 events must occur

So one possible combination aould be B1, C1, C2, A1, B2, A2

How many such combinations are there? I can work it out by hand but can't find the formula that would allow me to calculate it or even extend this to more than 3 paired events or figure out the combinations for n grouped events (so n groups of x events for a total of n*x events...in the initial case n=3 x=2)

Can anyone can point me in the right direction to get me started on solving this?

Thanks,
Nick
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August 2nd, 2009, 04:04 AM   #2
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Re: Determining the number of combinations for n paired events

Let's first look at the A-events. If you chose two of the six places then you can put the A-events on that places in exactly 1 way. So there are ways to place the A-events. For the B-events then there are still ways and for the C-events ways. The total is then combinations.
The generalisation is:
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