Specific items together

Questions asking for the probability that specific named items or groups are adjacent/next to each other in an arrangement.

5 questions · Moderate -0.2

5.01a Permutations and combinations: evaluate probabilities
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OCR S1 2005 January Q8
10 marks Moderate -0.8
8 An examination paper consists of 8 questions, of which one is on geometric distributions and one is on binomial distributions.
  1. If the 8 questions are arranged in a random order, find the probability that the question on geometric distributions is next to the question on binomial distributions. Four of the questions, including the one on geometric distributions, are worth 7 marks each, and the remaining four questions, including the one on binomial distributions, are worth 9 marks each. The 7-mark questions are the first four questions on the paper, but are arranged in random order. The 9-mark questions are the last four questions, but are arranged in random order. Find the probability that
  2. the questions on geometric distributions and on binomial distributions are next to one another,
  3. the questions on geometric distributions and on binomial distributions are separated by at least 2 other questions.
OCR Further Statistics AS 2019 June Q4
7 marks Moderate -0.3
4 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.
  2. Find the probability that no two men are next to one another.
OCR Further Statistics 2024 June Q6
11 marks Standard +0.3
6 A bag contains 6 identical blue counters and 5 identical yellow counters.
  1. Three counters are selected at random, without replacement. Find the probability that at least two of the counters are blue. All 11 counters are now arranged in a row in a random order.
  2. Find the probability that all the yellow counters are next to each other.
  3. Find the probability that no yellow counter is next to another yellow counter.
  4. Find the probability that the counters are arranged in such a way that both of the following conditions hold.
OCR FS1 AS 2017 December Q2
7 marks Moderate -0.3
2 Each letter of the words NEW COURSE is written on a card (including one blank card, representing the space between the words), so that there are 10 cards altogether.
  1. All 10 cards are arranged in a random order in a straight line. Find the probability that the two cards containing an E are next to each other.
  2. 4 cards are chosen at random. Find the probability that at least three consonants ( \(\mathrm { N } , \mathrm { W } , \mathrm { C } , \mathrm { R } , \mathrm { S }\) ) are on the cards chosen.
SPS SPS FM Statistics 2025 April Q5
7 marks Standard +0.3
An examination paper consists of 8 questions, of which one is on geometric distributions and one is on binomial distributions.
  1. If the 8 questions are arranged in a random order, find the probability that the question on geometric distributions is next to the question on binomial distributions. [2]
Four of the questions, including the one on geometric distributions, are worth 7 marks each, and the remaining four questions, including the one on binomial distributions, are worth 9 marks each. The 7-mark questions are the first four questions on the paper, but are arranged in random order. The 9-mark questions are the last four questions, but are arranged in random order. Find the probability that
  1. the questions on geometric distributions and on binomial distributions are next to one another, [2]
  2. the questions on geometric distributions and on binomial distributions are separated by at least 2 other questions. [3]