recategorized by
1 votes
1 votes

Three husband-wife pairs are to be seated at a circular table that has six identical chairs. Seating arrangements are defined only by the relative position of the people.  How many seating arrangements are possible such that every husband sits next to his wife? 

  1. $16$
  2. $4$
  3. $120$
  4. $720$
recategorized by

1 Answer

0 votes
0 votes

Every husband sits next to his wife, so we can say every husband-wife is a one-block.

There are $3$ husband-wife pairs, and each pair can sit in $2$ ways (Husband-Wife or Wife-Husband). The total number of seating arrangements is $2^3 = 8$ for each pair.

Now, consider these $3$ pairs as one unit each and arrange them in a circle, which can be done in $(3-1)!$ ways.

So, the total seating arrangements $= (3-1)! * 2^3 = 2 * 8 = 16.$

Correct Answer: A

Answer: