Three boys and three girls are going to eat dinner together in restaurant that only has round tables. One of the girls, Gena, does not want to sit next to a boy and Fred does not want to sit next to a girl.
Since Fred has to be in the middle of the boys, we can arrange the boys in 2 ways.
Similarly, girls can also be arranged in 2 ways.
Therefore, we found 2*2=4 different ways to arrange the boys and the girls.
The only other way to create a different arrangement of them would be to turn the table in one of the 4 arrangements. However, since we have no fixed point of reference, turning the table does not generate a different permutation of boys and girls from our perspective. Therefore, the number of possible arrangements is 4.
