Segments containing C are: AC, BC, CD, AD, BD
Segments not containing C are: AB
Any time the letter C is used to name the segment, point C is automatically on the segment (as one of the endpoints). So that accounts for AC, BC, CD including point C. Both AD and BD involve C as well since C is between the endpoints.
Only segment AB doesn't involve C as an endpoint, and C is not between A and B.