Combinatorics Question with limitations

Combinatorics Question with limitations

ol li$n$ men $\rightarrow n \in N$/li li$n$ women $\rightarrow n \in N$/li
li$n$ childs $\rightarrow n \in N$ br/li /ol pHow many ways we can order
them:( lets say in row )br/p ol liwithout limit/li li1 man and 1 woman
can`t sit togather/li lieach group sit togather, women, men , childs/li
li2 kids cannot sit togather/li libetween 1 man and 1 women there is at
least $3n-3$ people/li /ol pwhat I did so far is: ( my answers for each
question )br/p ol li$(n!)^3$/li li$\binom {n} {n-2} \cdot ((n-1)!)^2 \cdot
n!$/li li$(n!)^3\cdot (3!)$/li /ol pfor the two other I would like to get
some advice, and for what I answered comments.br thanks!/p