Hey Veeky Forums, combinatorics brainlet here, I have a group chat with 9 people in it...

Hey Veeky Forums, combinatorics brainlet here, I have a group chat with 9 people in it. How can I calculate how many groups of 2,3,4 and so on (different people) are possible? Ty (pic unrelated)

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1 group of 9 people

2^9-1

>how many groups of 2,3,4 and so on (different people)
You need to clarify this.

Groups of 2:
There are 9! permutations of the 9 ppl, and each group can be permuted in 2! ways. This means you have (9!/2!) groups of 2 people.

You get the pattern I think.

If you are a visual person, try imagining your 9 ppl aligned horizontally in a row, and each permutation is also a row, and all rows are arranged vertically. Rows are 'permuted atoms', you cannot split them in break them in pieces. When you divide by 2, it's as if you divide the permutations into 2 groups, each of which has an equal number of permutation atoms. You can pair each permutation of a group with a permutation of another group without leaving any permutation unmatched because 9! = 1*2*3*...*9 is an even number. If you imagine a match is putting one permutation over another, then you can see each people in the top permutation is paired with someone in the bottom permutation. So this process describes the number of groups of 2 ppl you can make from 9 ppl, 9!/2!

Suppose a group has just 2 people. The 1st can be any of 9, the 2nd any of 8. So 72 possibilities. But C&G is the same as G&C, so 36 possible groups.
3 person groups can be chosen 9*8*7 ways but, since order within the group doesn't matter, the 1st out of the group of 3 could be any of 3, the 2nd any of 2.

In general, the number of N person sub-groups is 9! / (9-N)! / N! where the "!" signifies "factorial".
N factorial is N*(N-1)*(N-2)......*1 Any decent calculator has a factorial key. 9! = 362,880 0! is defined as 1.

Evaluate the function for 2 though 9 and add your answers.

I think you're wrong. My reasoning is .
Either that or one of us in mis-understanding the question.

I made a picture because I can't english

I think you're right, but I can't see why I'm wrong. I was always bad with combinatorics

t. branlayt

OP, look at combinations.

en.wikipedia.org/wiki/Combination

actually wont it be combinatorial? like op how many groups can you make with all the 9 people? only one. and 9!/(9-9)! =/= 1 but 9!/(9-9)!9! = 1

and with this logic so does the rest, but for now think groups of 2,think like this, say person x, with how many other people can you pair him? the 8 others, then the next guy can only be paired with the other 7...etc etc... so you get
8+7+6+5+4+3+2+1=36 and 9 combinations per 2 is 36 and not arrangementes like you guys are saying

9!/(9-2)!2! = 36
9!(9-2)! = 72

Thanks a lot anons! Any idea on how I can relate this with the symmetry group?

no brainlet, there are 9*8 groups of 2 possible
for every person you choose there are 8 people left to choose from, you can choose the first person 9 times so 9*8 = 72

divided by 2! of course since we don't want repeats

so we getting 36, so the correct a answer is 9 combinations per x, being x the number of people the groups are made of

2 people you can make 36 groups
3 people you can make 84
4 people you can make 126
5 people you can make 126
6 people you can make 84
7 people you can make 36
8 people you can make 9
9 people you can make 1

being the equation 9!/(9-x)!x!

Don't understand your first sentence, but the numbers look right.
And you missed a "/" when you wrote out the equation.

sorry not native speaker so its kinda hard to translate certain terms, i tried looking out for it but i failed it seems.

where did i miss the "/"?

jesus mate you already were given a detailed answer: en.wikipedia.org/wiki/Combination

hit that nCr button on your calculator senpai

this is a very complex group theory problem

That's the Akira Supreme jumper
Good shit OP

Thanks man, a friend got this, so dope.