There are 5 married couples and a group of three is to be formed out of them; how many arrangements are there if a husband and wife may not be in the same group?
if you mean "Arrangements" , its a totally different question.
i assume ,you meant # of ways to select three people so that a couple in not there in a group.
Required answer = total # of ways - # of ways in which a couple are in a group.
1. Total # of ways = 10C3 ( 5 couples...ten people) = 120
2. # of ways a couple can be selected = 5C1
* 8C1 = 40 ways
Select one couple out of the five ..and select one person out of the rest
of the 8.
3. required answer = 120 - 40 = 80 ways
EDIT : thanks BG... correction made with bold part