In how many different ways can six boys and six girls be arranged in a single row for a photograph such that no two girls are seated next to each other?

Explanation

First, arrange the six boys in 6! different ways. This creates seven potential spots around them where the girls can be placed without sitting together. Since there are six girls and seven available positions, the girls can be arranged in 7P6 ways. Therefore, the total number of arrangements is 6! × 7P6, which equals (6!)².