In how many ways can 4 married couples seat themselves around circular table if at least one husband sits beside his wife?
To solve this problem, we can use the principle of inclusion-exclusion.
First, let's consider the number of ways to seat the 4 couples without any restrictions. Each couple can be seated in 2 ways, so the total number of ways to seat them is 2^4 = 16.
Next, let's count the number of ways where no husband sits beside his wife. We can think of this as treating each couple as a single entity and seating them around the table. There are 4 entities to seat, and they can be arranged in a circular pattern in (4-1)! = 3! = 6 ways.
Therefore, the number of ways where at least one husband sits beside his wife is the total number of ways minus the number of ways where no husband sits beside his wife. Therefore, the answer is 16 - 6 = 10.
So, there are 10 ways to seat the 4 married couples around the circular table if at least one husband sits beside his wife.