How many ways can we put 7 adults and 3 kids in line (where order matters) so that no two kids are next to each other?

Given that the order matters in this question, we shall apply the concept of permutation rather than computation. Thus, the number of ways in which that we can put 7 adults and 3 kids in line will be:

7P3

=210

There are more than 210 ways we can do this.