Number of gatherings possible?

Question

Given that $n$ couples were invited to a party, based on the following conditions:

• Husbands can attend the party only when they are accompanied by their respective wives.
• Wives need not be accompanied by their husbands to attend the party.

How many gatherings are possible?

If they are $n$ couples, there are $2n$ people. That is all I can think of. With that fact in mind I tried to approach the problem by working out all possibilities. Obviously, I am going nowhere with that approach.

How do I approach this problem?

Any suggestions?

Answer 1

Hint: For each couple there are $3$ possibilities. That is,

• The husband and wife, both attend the party
• Only the wife attends the party
• None of them attend the party