PK 2015 Q18
18. Petra has three different dictionaries and two different novels on a shelf. How many ways are there to arrange the books if she wants to keep the dictionaries together and the novels together?
- A 12
- B 24
- C 30
- D 60
- E 120
Pink Kangaroo 2015, Question 18. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 24
Petra can arrange the dictionaries in six ways (3 choices for the first dictionary, 2 choices for the second dictionary, 1 choice for the third, giving 3 × 2 × 1 = 6 ways). The novels can be arranged in two ways. Since the novels could be on the left of the dictionaries, or on the right, we have a total of 6 × 2 × 2 = 24 ways to arrange the books.
Solution © UK Mathematics Trust, from the PK 2015 solutions.