How many different combinations of order can a family take a photo in?

Question

There is a family of 6. A mom, a Dad, and 4 children. In a family photo they must stand in a line without either parent standing on either end of the line. How many ways can they stand for the picture?

Answer 1

Place a child at the far left; 4 choices

Place a child at the far right: 3 choices

four remaining persons may be arranged in 4! ways at the remaining positions.

 

Product of all these is 4(3)(4!),,,you compute it.