59. Three distinct lines, all contained in a plane, separate the plane into distinct regions. What are all of the possible numbers of distinct regions of the plane that may be separated by any 3 such lines?

(Note: Do NOT include any of the points on the 3 lines in your count of distinct regions.)

Answer and Explanation

Your Answer is

Correct Answer is E

Explanation

Three lines are parallel, divide the plane into 4 parts; two lines are parallel, and another side intersects them, or three lines are not parallel but intersect at the same point, and there are 6 pieces; three lines are not parallel and have no common intersection point , get 7 copies. Therefore E.