Permutations Problem

Question

How many ways are there to seat 5 adults and 6 children in a row of chairs so that no kids sit together?

Explain please with steps for a better understanding!

Answer 1

Make the 6 children sit in alternate chairs. That can be done in 6! ways

Now 5 chairs between the 6 children which can be filled by the adults in 5! ways.

By the fundamental counting principle the arrangements can be made in 6! 5! ways.

Answer 2

Two separate groups, 5 adults and 6 children

5 adults can be seated 5! ways

6 children can be seated 6! ways

(5!)(6!) = ?