1.1 Two couples want to sit on a bench. In how many ways can they sit so that each boy sits next to his girlfriend, if the left and right sides of the bench are distinguishable?
# Answer: 8

Solution. Let's number the seats from 1 to 4. If one of the couple sits in seat number 1, then the second must sit in seat 2. Thus, each couple either sits on the left (seats 1 and 2) or on the right (seats 3 and 4). Each couple can sit in two ways (boy on the left or right), and the couples themselves can switch places. In total, $2 \cdot 2 \cdot 2=8$ ways.