In how many ways can you split six persons in two groups?
I think that I should use the binomial coefficient to calculate this but I dont know how.
If the two groups has to have equal size, then each group should have three persons. Then the calculation would be:
$${{6}\choose{3}}/2 = 10$$
But since the groups now can have different sizes I dont really know. I would guess that you have to add up multiple binomial coefficients, something like this:
$$ {{6}\choose{1}} + {{6}\choose{2}} + {{6}\choose{3}}=41$$
But the answer should be 31 so that does not seems to be quite right. I would like some suggestions on this!
Best Answer
I assume the two groups must be non-empty! It helps to know that Alicia is one of the people.
Joining Alicia will be any subset of the remaining people, except for the full set. So there are $2^5-1$ ways to choose the people who will be in Alicia's group.