I was trying to solve the following problem:
Eight persons, consisting of four male-female couples, are to be seated in a row of eight chairs. How many seating arrangements are there in each of the following cases:
- There are no other restrictions.
- The men must sit together and the women must sit together.
- The men must sit together.
- Each couple must sit together.
For the first and forth points I was able to find a solution easily (respectively $10*9*8$ and $8*6*4*2$), but for the other middle points I am having some little troubles. Doesn't the 3rd point imply the second?
In both cases, the first person will have $8$ places to choose from, but the second person that seats will have to be careful depending on the first person was a male or a female and depending if it is a male or a female.