number of combinations possible

I would like to figure out the total number of combinations in the below examples. Not a math person, so sorry if my terminology is strange.


I have sets of 8 pieces, lets say pieces numbered 1-8. I have 50 total of these sets, set 001 - 050... so 50 sets with 8 pieces numbering 1 - 8, sets numbered 001 - 050 (for example).

I want to combine these sets of 8 by 2. I will combine 50 sets together but only two at a time. Set 001 combined with set 002, set 005 combined with set 042, and so on randomly. The result will be a new set of 8 places combined randomly from the two sets of pieces. Also, you can only combine a piece 1 with another piece 1, a 2 with a 2 and so on, otherwise it is random. So the result will be a random combination based on the two sets, where each place 1 -8 is a random selection of two possible pieces.

Additionally I would like to figure out how many combinations I could get by combining the entire group of 50 sets into randomly combined sets containing pieces 1 - 8. Where you can only place 1 - 8 in it's proper place in the resulting set, so the same as above but with more pieces to choose from. So in this model, for piece 1 you would have 50 total random choices. The same goes for each of the other pieces 2, 3, 4, 5, 6, 7, and 8, you would have a total of 50 random pieces to select from for each place.

I hope this question makes sense, and there is someone who can point me in the right direction.

Thanks!!!

Mr Wolfy(Bow)

I see that no one else has tried to help. Perhaps it is the wording.
Frankly, I don’t know exactly what the question means.

But here is maybe a start.
If we have fifty individuals the number of possible pairs is: $\displaystyle \frac{50!}{(2^{25})(25!)}$.
That is in itself a huge number with at least 30 digits.

I hope that helps you.