number of ways to seat n couple in row of 2n chairs so that

[wheatwoman]

In how many ways can n married couples be seated in a row of 2n chairs with no husband seated next to his wife?

Every other seat could be a !(factorial) but I'm not sure how to do it.

Any help would be appreciated.

 

[Denis]

Re: Discrete Math Question

Go here: http://www.research.att.com/~njas/sequences/index.html
and enter 0,8,240,13824 in search box.

 

[Deleted member 4993]

Re: Discrete Math Question

In how many ways can n married couples be seated in a row of 2n chairs with no husband seated next to his wife?

Every other seat could be a !(factorial) but I'm not sure how to do it.

Any help would be appreciated.

Hint:

Tie two chairs together (make loveseat) - total n love-seats. Tie the couples together - real tight.... :wink:

Now how many ways can you seat 'n' "tied" couples in 'n' love-seats.

Then think.....

 

[pka]

The best way to approach this question is to first calculate the number of ways to have at least one couple is seated together.
\(\displaystyle \sum\limits_{k=1}^n {\left( { - 1} \right)^{k + 1} { n \choose k} \left( {2n - k} \right)!\left( {2^k } \right)}\). (Take note of the powers of 2: HF or WH)

Now subtract that number from the total possible, \(\displaystyle (2n)!\).