I am studying for the GRE and reviewing a fair amount of pre-college math. I have a problem involving combinations, and have worked out a solution that I want to check on this forum. I've put my answer below, so just look at the question if you want to try it for yourself. Let me know if there is a faster way to do this too, please.
===== QUESTION =====
Anne and Mark want to invite 5 friends to a dinner party. Anne has 7 friends, and Mark as 6 friends. They have no friends in common. If each of them must have at least 2 friends at the party, how many combinations of guests are possible?
===== MY ANSWER ======
Find the total possible combinations and then subtract those that do not meet the two friend each criteria...
13C5 = 1287 (Total possible combos) --- Invalid Combos --- 7C4 * 6C1 = 210 (Combos with 4 of Anne's friends, but only one of Mark's) 6C4 * 7C1 = 105 (Combos with 4 of Mark's friends but only one of Anne's) 7C5 = 21 (Combos with just Anne's friends) 6C5 = 6 (Combos with just Mark's friends)
So we subtract the invalid possibilities from total possibilities, and get 945.