Hi,
Let us label the guys 1, 2, 3 and so on up to 12.
Case 1: Let 1 be the first member of the group.
1,3,5,_ -> 6 ways
1,3,6,_ -> 5 ways
1,3,7,_ -> 4 ways
1,3,8,_ -> 3 ways
1,3,9,_ -> 2 ways
1,3,10,_ -> 1 way
1,4,6,_ -> 5 ways
1,4,7,_ -> 4 ways
1,4,8,_ -> 3 ways
1,4,9,_ -> 2 ways
1,4,10,_ -> 1 ways
In a similar manner, 1,5,_,_ -> 4+3+2+1 = 10 ways
1,6,_,_ -> 3+2+1 = 6 ways
1,7,_,_ -> 2+1 = 3 ways
1,8,_,_ -> 1 way only.
Thus, if '1' is included, there are 21 + 15 + 10 + 6 + 3 + 1 ways (56 ways) of having 4 people.
Case 2: Let 2 be the first member of the group.
2,4,6,_ -> 5 ways
2,4,7,_ -> 4 ways
Thus, 2,4,_,_ -> 15 ways
2,5,_,_ -> 10 ways
2,6,_,_ -> 6 ways
2,7,_,_ -> 3 ways
2,8,_,_ -> 1 way
Thus, if '2' is included, there are 15 + 10 + 6 + 3 + 1 ways (35 ways) of having 4 people.
Case 3: If 3 is the first member of the group, there are 10 + 6 + 3 + 1 ways (20 ways) of having 4 people.
Case 4: If 4 is the first member of the group, there are 6 + 3 + 1 ways (10 ways) of having 4 people.
Case 5: If 5 is the first member of the group, there are 3 + 1 ways (4 ways) of having 4 people.
Case 6: If 6 is the first member of the group, there are 1 ways (1 way) of having 4 people.
Overall total = 56 + 35 + 20 + 10 + 4 + 1 = 126 ways.
