Divide 17 people into two groups, one with 12 and one with 5 people
a) Person a and Person b have to be in different groups
- For this question I think that for every ordered group of 12 there will be and unordered group of 5, so the answer should be 15c12
b) Person a and Person b have to be in the same group
- Here I'm not as sure, I tried drawing it out, is it just answer a divided by two?
Hint:
For a) Suppose that you already put $a$ in group 1 and $b$ in groups 2. Then you need to find the number of ways to divide 15 people to 2 sets, one with 11 people and the other with 4 people. Do the same with $a$ in group $2$ and $b$ in group $1$ and sum up.
For b) Suppose that $a,b$ in group $1$, so you need to find the number of ways to divide 15 people to $2$ sets, one with $10$ people and the other with $5$. Then take $a,b$ in group $2$ and formulate a similar question. Once you solved both sum up the results.