1. The problem statement, all variables and given/known data 12 subjects (6 male, 6 female) are put on 3 lines, 4 in each. In how many ways can this be done, if one of the males and one of the females want to be on the same line? 2. Relevant equations None. 3. The attempt at a solution I thought it like this. I can pick the first 10 spots and leave the lovebirds behind. That can be done in 2 * (4C2) * 4! * 4! = 6912. 2*(4C2) because I'm picking spots for the two on the line where the lovebirds are missing, and they can be switched places so I multiply by 2. 4! * 4! is for the normal lines. When I add the lovebirds to this, I get 6912 * 3 * 2 = 41472 because the unfinished line could be any of the 3, and multiply by 2 because, for each possibility in 4C2 above, I could have just put the couple there and switched them inwards.