Question

Let $m$ be the number of ways in which two couples can be seated on $4$ chairs in a row so that no wife is next to her husband and $n$ be the number of ways in which they can be seated in $4$ chairs in a circle. In the latter case, rotations are considered different configurations. Then

• A. $m=n$
• B. $m=2n$
• C. $m=4n$
• D. $m=8n$

Answer 1

The correct option is A $m=n$

For first situation, there are two choices shown

So, $m=2$

For second situation we have $2$ choices

So, $n=2$

Therefore, $m=n$