This is the problem in question:
Suppose $18$ different people are standing in line waiting for the grand opening of IKEA. There are $6$ men, $8$ women, and $4$ children. In how many ways can they line up if the first woman appears ahead of the first child?
I am thinking of creating a woman-child object, which can be done $8 \cdot 4$ ways. Then, place the remaining $7$ women and $3$ children to the right of that object. Finally, place the men into the slots. What I am having trouble with is determining how to represent placing $7$ women and $3$ children to the right of the object.
$8 \cdot 4$ ways to create the woman-child object.
$11!$ ways to arrange $7$ women and $3$ children.
Do I divide $11!$ by $2$? Will that means they must appear on one side?