Ménehould is organizing a birthday party, which will have 15 girls and 15 boys (including herself). She is preparing a personal label for each guest. In how many ways can she arrange the labels on the seats of the round table while maintaining the alternation of girl-boy?
There are $2 \times 15$ ! ways to seat the boys, and for each of them, 15 ! ways to seat the girls. The result is $2 \times(15 \text { ! })^{2}$.