| Date | May 2013 | Marks available | 4 | Reference code | 13M.2.hl.TZ1.8 |
| Level | HL only | Paper | 2 | Time zone | TZ1 |
| Command term | Find | Question number | 8 | Adapted from | N/A |
Question
Three boys and three girls are to sit on a bench for a photograph.
Find the number of ways this can be done if the three girls must sit together.
Find the number of ways this can be done if the three girls must all sit apart.
Markscheme
the three girls can sit together in 3! = 6 ways (A1)
this leaves 4 ‘objects’ to arrange so the number of ways this can be done is 4! (M1)
so the number of arrangements is \(6 \times 4! = 144\) A1
[3 marks]
Finding more than one position that the girls can sit (M1)
Counting exactly four positions (A1)
number of ways \( = 4 \times 3! \times 3! = 144\) M1A1 N2
[4 marks]
Examiners report
Some good solutions to part (a) and certainly fewer completely correct answers to part (b). Many candidates were able to access at least partial credit, if they were showing their reasoning.
Some good solutions to part (a) and certainly fewer completely correct answers to part (b). Many candidates were able to access at least partial credit, if they were showing their reasoning.
