18. Find the number of ways for 5 persons to be seated at a rectangular table with 6 seats, 2 each on the longer sides and 1 each on the shorter sides. The seats are not numbered.
18. Answer: 360
The empty seat can be considered to be a person. Now the number of ways of sitting at a round table is $(6-1)!=120$. Note that each arrangement at a round table can be matched to 3 different arrangements at the rectangular table. Thus the number of ways of sitting at the rectangular table is $3 \times 120=360$.