| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2011 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Permutations & Arrangements |
| Type | Arrangements with adjacency requirements |
| Difficulty | Moderate -0.3 This is a standard permutations question with typical adjacency constraints. Part (i) involves basic factorial counting and treating two people as a single unit (standard 'gluing' technique). Part (ii) requires arranging boys and girls with restrictions, using gap methods and block arrangements—all textbook techniques for S1. While multi-part, each component is routine and requires no novel insight, making it slightly easier than average. |
| Spec | 5.01a Permutations and combinations: evaluate probabilities5.01b Selection/arrangement: probability problems |
6 A group of 7 students sit in random order on a bench.\\
(i) (a) Find the number of orders in which they can sit.\\
(b) The 7 students include Tom and Jerry. Find the probability that Tom and Jerry sit next to each other.\\
(ii) The students consist of 3 girls and 4 boys. Find the probability that\\
(a) no two boys sit next to each other,\\
(b) all three girls sit next to each other.
\hfill \mbox{\textit{OCR S1 2011 Q6 [9]}}