Arrangements with adjacency constraints

Arrange people or objects in a line or row where certain individuals must be next to each other, or must not be next to each other, or specific groups must stand together.

2 questions · Standard +0.6

5.01a Permutations and combinations: evaluate probabilities
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OCR Further Statistics AS 2023 June Q2
7 marks Standard +0.8
2 A music lover has 30 CDs arranged in a random order in a line on a shelf. Of these CDs, 7 are classed as Baroque, 10 as Classical and 13 as Romantic.
  1. Determine the probability that all 7 Baroque CDs are next to each other.
  2. Determine the probability that, of the 10 CDs furthest to the left on the shelf, at least 6 are Baroque.
SPS SPS ASFM Statistics 2021 May Q3
7 marks Standard +0.3
The members of a team stand in a random order in a straight line for a photograph. There are four men and six women.
  1. Find the probability that all the men are next to each other. [3]
  2. Find the probability that no two men are next to one another. [4]