In how many ways can you seat 4 couples at a round table if:

1) each couple sits together?

2) no couples sits together?

you have 8 people. 8 chairs

1. If the couple has to sit together then...the first chair has 8 possible ways, but the next one can only have 1 possible way which is the persons significant other. You have 6 chairs left and the 3rd chair now has 6 possible ways, and the next one to it has only 1...and etc... so...

8 * 1 * 6 * 1 * 4 * 1 * 2 * 1 = 384 ways.

2. the total possible ways to seat these 4 couples with no restrictions...

8! = 40320

if no couples sits together....then you take the total possible ways minus the possible ways of them sitting together.

8! - 384 = 39936