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This is just a question I came up with. Let's say there are just two genders and we want to know how many possible gender combinations a couple chosen at random can have, that is order doesn't matter? It is easy to solve this by making an ordered list and eliminating one of the repeating pairs of man and woman. The answer is 3. But my question is let's say there are three genders, trans gender being the third one and in this world the norm is for three people to be in a relationship; whatever relationship there is there are three people in it. Making an ordered list is messy. What other way is there to find the number of possible gender combinations a group of three people can have? By making an ordered list I got the answer 5. Also, please tell can the first question be solved without making ordered list?

Also, if I use the fundamental counting principle for the two gender question, I will have 2X2= 4 possibilities, which doesn't give the correct answer. If I use the combination formula 4 (Male Female for spot 1 and Male Female for spot 2) choose 2 spots or 4!/(2!X2!), I get the answer as 6.

Abhinav
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  • what do you mean by “possible gender combinations a couple chosen at random can have”? more specifically, what do you mean by “gender combination”? – C Squared Jul 07 '21 at 11:22
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    This sort of problem can be solved by stars and bars. (https://en.wikipedia.org/wiki/Stars_and_bars_(combinatorics)) – saulspatz Jul 07 '21 at 11:24
  • It's more like programming.. You want to build an application. Where you will have lot of list of people then, you just want to combination them. That's what I think!! You can use some easy algebraic expression.. –  Jul 07 '21 at 11:25
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    @Istiak No, this is a straightforward combinatorics problem. – saulspatz Jul 07 '21 at 11:25
  • https://artofproblemsolving.com/community/c3h566981p3320664 – saulspatz Jul 07 '21 at 11:30
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    @CSquared, I meant what are the possible gender combinations as in Male Female, Male Male, Female Female. – Abhinav Jul 07 '21 at 11:45
  • I keep getting the answer $10,$ rather than $5.$ But then, I always was confused about gender. :) – Calum Gilhooley Jul 07 '21 at 12:37

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