68. In how many ways can 5 girls and 5 boys be seated at a round table so that no two people of the same gender sit next to each other?
68. Let's renumber the seats at the round table from first to tenth. We will seat the boys in the seats with odd numbers, and the girls in the seats with even numbers. This can be done in (5!) ${ }^{2}$ ways. We will get the same number of ways if we switch the boys and girls. Ultimately, we will have $2(5!)^{2}=28800$ ways.