1. A family consisting of two parents and four children is to be seated in a row for a picture. How many different arrangements are possible in which the children are seated together?
2. If 10 lines are drawn in the plane so that no two of them are parallel and no three lines intersect at the same point, how many points of intersection are there?
3. Two elementary school teachers have 24 students each. The first teacher splits his students into four groups of six. The second teacher splits her students into six groups of four. Which teacher has more options?