OCR S1 2011 June — Question 6 9 marks

Exam BoardOCR
ModuleS1 (Statistics 1)
Year2011
SessionJune
Marks9
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPermutations & Arrangements
TypeArrangements with adjacency requirements
DifficultyModerate -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.
Spec5.01a Permutations and combinations: evaluate probabilities5.01b Selection/arrangement: probability problems

6 A group of 7 students sit in random order on a bench.
  1. (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.
  2. 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.

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]}}