SOLUTION: what is the number of ways of seating 3 men and 5 women in a row if there is no restrictions

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Question 1046062: what is the number of ways of seating 3 men and 5 women in a row if there is no restrictions
Found 3 solutions by KMST, ikleyn, MathTherapy:
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Consider how the women are lined up .
There are 5%21=5%2A4%2A3%2A2=120 different ways to line up those 5 women.
Considering how the men are lined up,
there are 3%21=3%2A2=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%2B3=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%2A7%2A6%2F%283%2A2%29=56 such combinations of 8 taken 3 at at time.
So, out total number of choices is
120%2A6%2A56=40320 .

Answer by ikleyn(52781) About Me  (Show Source):
Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

what is the number of ways of seating 3 men and 5 women in a row if there is no restrictions
1st position: 8 persons

2nd position: 7 persons, and so on

This means that there are: highlight_green%28matrix%281%2C4%2C+8%21%2C+or%2C+%2240%2C320%22%2C+ways%29%29