816 different three member committee combinations are possible .
With 18 total members, 3 members per committee means 18/3 = 6. There are AT LEAST 6 groups with 3 members. The different combinations of members in each group is where the combinations increase.
To visualize, if each number is a person, look at some different groups that can be made:
1,2,3
4,5,6
7,8,9
10,11,12
13,14,15
16,17,18
Also:
18,15,12
9,6,3
2,5,8
11,14,17
1,4,7
10,13,16
That’s already 12 groups with different people. So there will be a lot more.
So, if you use the combinations formula:
18!/(3(18-3)!)
Which simplifies to:
18!/(3!*15!)
= 816.