4. Five pairs of comic characters, Donald and Katrien Duck, Asterix and Obelix, Suske and Wiske, Tom and Jerry, Heer Bommel and Tom Poes, sit around a round table with 10 chairs. Each pair ensures that the two members sit next to each other. In how many different ways can the ten chairs be occupied? Two ways are different if they cannot be transformed into each other by a rotation.
4. Donald and Katrien can sit next to each other at a table. The eight remaining seats can be seen as four pairs of seats where each pair of seats will be occupied by a couple.

This gives for the possible distributions of the couples $4 \times 3 \times 2 \times 1=4$ ! possibilities.

For each couple, there are still 2 possibilities. So in total $4 ! \times 2^{5}=768$

possibilities.