I'm doing the question 1.10 from the Ross text and can't figure out how to get the answer they provide. The question is:
"A woman has 8 friends, of whom she will invite 5 to a tea party. How many choices has she if 2 of the friends are feuding and will not attend together? How many choices has she if 2 of her friends will only attend together?"
I know that to select 5 out of the 8, it's 8 choose 5 or (8*7*6*5*4)/(5*4*3*2*1). But I can't figure out how to make sure that friends A and B are not together. I know that it's not necessarily the case that these women will even be part of the 5. Can you suggest the next step?