help

[jade bloom]

help

[regal flower]

Yay, more vaguely described combinatorics.

are the tables distinct? is AB vs CD at table 2 the same as AB vs CD at table 7?

are the positions at the tables distinct? E.g. if it's spades/bridge, somebody deals first, bids first and bidding goes clockwise.

If no symmetries are clearly defined, it will be (4n)! but I highly doubt that is your sloppy teacher's intention.

[regal flower]

!original

[inner nymph]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[regal flower]

there is a really good chance we're going in that direction

[jade bloom]

I just need to knwo hwo to set the mutlinomila up and i am good

[regal flower]

why 4n-4?

step 1? show me everything so I can be effective

the multinomial you presented is like
I have 4n-4 unique marbles to put in n-1 unique bags. How many ways can I put 4 in each

[regal flower]

The way I look at things:
what is independent? tables
what is symmetrical?

If nothing is symmetrical, I have an n-array of 4-arrays with cardinality (4n)!

what symmetries exist?
How is a 4-array different than something less complicated?
4-array --> 4-bag (4! --> 1)

the multinomial coeficient

puts n things into m bags of k_m size

for us it would be (4n)! / (4!)^n

tables? if table doesn't matter? n-array --> n-bag. |n-array| = n! |n-bag| = n! //n-bag = 1 for all n
n-bag of 4-bags has cardinality (4n)! / [n! (4!)^n]

the real questions what is the original question?
what are the 4's symmetry?
4-array? 2-array of 2-arrays? 4!
4-bag? 1
2-array of 2-bags? 4!/(2!)^2 = 4C2
2-bag of 2-bags? 4!/(2!)^3 = 4C2 / 2P2

Turn the original question into the language of combinatorics and it's one these

[regal flower]

what does this mean?

n-array of 2-bags of 2-bags?

the 3^n implies you're accounting for something

do you understand my array vs bag notation?

the question isn't clear, we need to state our assumptions to give an answer

2-bags of 2-bags = 3
//a player and one of 3 potential partners in one bag, the other bag is implied

2-bag of 2-bag //no difference between teams, no difference between first or second player on a team
2-bag of 2-array // no difference between teams, first player on each team is important
2-array of 2-bag // who is on which team is important, no difference between first or second player on a team

if "it does not matter which group sits at which table", then we haven't accounted for that symmetry but lets pause that discussion till we settle whats happening at each table

sorry no, I'm going to keep pushing the proper language until you start using it

does the order of the players on a team matter? yes-->array, no --> bag