A Committee Structure
We will consider a structure for creating committees that will be efficient
and effective in designing programmatic changes for all members of an organization.
Conditions for a Committee Structure

Each committee will have exactly three members.

Any two committees will have exactly one member in
common.

Any two members determine a unique committee.

There are at least two committees.
Here are two examples:
Notice that each structure has 7 committees and 7 members!
C 
E 
G 


G 
B 
C 
B 
D 
G 


G 
D 
F 
A 
F 
G 


G 
A 
E 
A 
D 
E 


C 
E 
D 
B 
F 
E 


D 
A 
B 
A 
B 
C 


C 
A 
F 
D 
F 
C 


B 
F 
E 
Interesting....these were the same arrangements used for the chord stuctures.
But the question we have now is:
Are there any of these committee
stuctures that have more or less than 7 committees made from 7 members?
That is, is there some special
relation between these committee structures and the number 7?