Observation

The Chief Examiner reported that this question was attempted by majority of the candidates and they performed better in part (b) than in part (a).

In part (a), candidates were reported not to interpret the question correctly. In part (a)(i), candidates were expected to show that if books on the same subject were to stand together, then taking the books in the same subject as one, there will be 3! ways of arranging the three sets of books. But within the various subject groups, the mathematics books can be arranged in 2! ways. Similarly, the physics and chemistry text books can be arranged in 5! and 3! ways respectively.

Therefore, the number of ways of arranging the books in a row if the books on the same subjects must stay together was 3! × 2! × 5! × 3! = 8640 ways. In part (a)(ii), taking all the physics books as one book, there will be 6 books to be arranged and this can be done in 6! ways. But the 5 physics books can be arranged in 5! ways. Therefore, the number of ways of arranging the books if the physics books must stay together = 6! × 5! = 86400 ways.