There are 2 decisions that can be made concerning friend #1, invite
friend #1 or don't invite friend #1. That's 2 ways.
There are 2 decisions that can be made concerning friend #2, invite
friend #2 or don't invite friend #2. That's 2 ways.
There are 2 decisions that can be made concerning friend #3, invite
friend #3 or don't invite friend #3. That's 2 ways.
There are 2 decisions that can be made concerning friend #4, invite
friend #4 or don't invite friend #4. That's 2 ways.
There are 2 decisions that can be made concerning friend #5, invite
friend #5 or don't invite friend #5. That's 2 ways.
There are 2 decisions that can be made concerning friend #6, invite
friend #6 or don't invite friend #6. That's 2 ways.
There are 2 decisions that can be made concerning friend #7, invite
friend #7 or don't invite friend #7. That's 2 ways.
Answer = 2∙2∙2∙2∙2∙2∙2 = 27 = 128 ways.
Edwin