6 A test consists of 4 algebra questions, A, B, C and D, and 4 geometry questions, G, H, I and J.
The examiner plans to arrange all 8 questions in a random order, regardless of topic.
- (a) How many different arrangements are possible?
(b) Find the probability that no two Algebra questions are next to each other and no two Geometry questions are next to each other.
Later, the examiner decides that the questions should be arranged in two sections, Algebra followed by Geometry, with the questions in each section arranged in a random order. - (a) How many different arrangements are possible?
(b) Find the probability that questions A and H are next to each other.
(c) Find the probability that questions B and J are separated by more than four other questions.