Question 1046062
Consider how the women are lined up .
There are {{{5!=5*4*3*2=120}}} different ways to line up those {{{5}}} women.
Considering how the men are lined up,
there are {{{3!=3*2=6}}} ways to line them up.
We could sit all 3 men at one end,
in what we could say are positions 1, 2, and 3, of the row of {{{5+3=8}}} people.
There are other ways to pick where the men would go.
Any set of 3 position numbers picked out of the 8 positions would do.
There are {{{8*7*6/(3*2)=56}}} such combinations of 8 taken 3 at at time.
So, out total number of choices is
{{{120*6*56=40320}}} .