Get your seat!
Probability
Level
2
In how many ways can 4 men and 4 women sit in 4 benches with 2 seats each, being that in each bench must have a man and a woman sat in it.
The answer is 9216.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
First we need to know that there is 8 possible seats divided in 4 different benches. Let the women choose their seats first.
The first woman have 8 possible ways to choose her seat.
The second woman will have 6 possible ways to choose her seat since she can't sit in the same bench of the first woman.
The third woman will have 4 possible ways to choose her seat since she can't sit in the same bench of the first two women.
The fourth woman will have only 2 possible ways to choose her bench.
Now let the men choose their seats.
The first man will have 4 ways to choose his seat.
The second man will have 3 ways to choose his seat.
The third man will have 2 ways to choose his seat.
And finally, the fourth man will have only 1 way to choose his seat.
In total we have 8 × 6 × 4 × 2 × 4 × 3 × 2 × 1 = 9 2 1 6 ways that these 8 people can sit in this benches following the conditions of the problem.