Thread: Looking for a formula for K Permutations (I think)

Hello! I know how to find K Permutations for 1 group of numbers, but I need a formula to find the total combinations possible using the following criterea.

5 groups of Numbers (with varying amounts of numbers in each group).

For example
Group 1 = 1,2,3,4,7,19,25
Group 2 = 5,7,15,29,35,40
Group 3 = 5,29,51,52,53,54
Group 4 = 19,22,23,24,25,32,27,28
Group 5 = 28,29,30,31,32,40,41

1 number from each group- using no duplicates in selections.
Need to find the total amount of 5 number combinations (such as 1 5 29 19 28).

Any help on a formula for this would be greatly appreciated.

I do not think that there can be an answer to such a vague question.
If the example you gave is the actual question then you must look at all the cases where the different collections have non-empty intersections.
For example, you can select any elements from the first two.
But then as you move to group 3, you must consider if from group 2 you have selected 5 or 29 then that restricts what you can pick in group 3.
So fourth and so on.

Short of having actual data sets, I see no way of giving a general solution.

I'm sorry. I'm not a mathematician, but I've always been under the impression that nothing is impossible. Perhaps someone who likes a challenge will put a little more effort into either solving my problem or providing a less vague description as to why it's not possible. If you want an actual data set, used the one in my example. That was it's intended purpose, I didn't just post it to waste space. As stated, the integers will vary, which is why I need a formula (like the one posted below) capable of handling those perameters, and not just a "quick-fix" for a high-school math problem.

I know that if I have a set of, say, 70 integers numbered 1-70, and I want to find the total number of 5 integer combinations, using no repeating integers, I use the following formula, where N is the size of the group and K is the size of each set of numbers.
N!
K!*(N-K)!

I would think that my problem would use some variation of this formula while perhaps taking into account the number of duplicate integers from one collumn to the next, or even overall, and then subtracting that from the equation in some way. If there's no way to do this with a mathmatical formula (no matter how complex), I'd be suprised. In that case, I'll build a PERL script to just randomly generate the sets until it times out.

Thanks for your... time.

The real difficulty as I explained above is that the groups overlap. But you require that the same number not be used more than once in any selection even if it was selected from different groups. This task can be done using computer programming. But it is not strictly a mathematical problem.

hmm...a programming problem is a mathematical problem i suppose...this seems to have a connection to my question...if you can build a program with PERL and find a formula then why can't you find an algorithm using pen and paper???in any case,can you tell me how would you think in order to build this PERL program?