Three Mathematics books, five English books, four Science books and a dictionary are to be placed on a student’s shelf so that the books of each subject remain together.

(a)     In how many different ways can the books be arranged?

(b)     In how many of these will the dictionary be next to the Mathematics books?

(a)     There are 3! ways of arranging the Mathematics books, 5! ways of arranging the English books and 4! ways of arranging the Science books.     (A1)

Then we have 4 types of books which can be arranged in 4! ways.     (A1)

\(3! \times 5! \times 4 \times 4! = 414\,720\)     (M1)A1

(b)     There are 3! ways of arranging the subject books, and for each of these there are 2 ways of putting the dictionary next to the Mathematics books.     (M1)(A1)

\(3! \times 5! \times 4! \times 3! \times 2 = 207\,360\)     A1

[7 marks]

Many students added instead of multiplying. There were, however, quite a few good answers to this question.