Four men and their wives were seated on a bench

[maya gebo]

Hey guys, how would you answer this if the four men and their wives were seated on a bench? Please help.

In how many ways can 4 married couples be arranged on a bench if"

a) Each man sits beside his wife and men and women alternate?

b) men and women alternate?

 

[MarkFL]

Hello, and welcome to FMH!

a) We have two cases to consider here (W = woman and M = man):

WMWMWMWM

MWMWMWMW

In both cases, how many objects are we arranging and what are these objects?

 

[pka]

How would you answer this if the four men and their wives were seated on a bench?
In how many ways can 4 married couples be arranged on a bench if"
a) Each man sits beside his wife and men and women alternate?
b) men and women alternate?

a) the four couples can be seated together in \(\displaystyle 4!\) times \(\displaystyle 2^4\) ways.
Can you explain why those are the answers?

b) \(\displaystyle 2(4!)^2\) Please explain that answer. Hint: "male/female or female/male".

 

[MarkFL]

a) the four couples can be seated together in \(\displaystyle 4!\) times \(\displaystyle 2^4\) ways.
Can you explain why those are the answers?

b) \(\displaystyle 2(4!)^2\) Please explain that answer. Hint: "male/female or female/male".

a) I get \(2\cdot4!\). How did you get \(2^4\cdot4!\)?

 

[pka]

a) I get \(2\cdot4!\). How did you get \(2^4\cdot4!\)?

Actually that is the answer to a different question: "How many ways the couples can sit together, without men and women alternate ?
I guess I did not read carefully.