Specific items separated

Questions asking for the probability that specific items are NOT together or are separated (e.g., no two men next to each other, vowels not all together).

6 questions · Standard +0.7

5.01a Permutations and combinations: evaluate probabilities
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CAIE S1 2011 June Q4
8 marks Moderate -0.3
4
  1. Find the number of different ways that the 9 letters of the word HAPPINESS can be arranged in a line.
  2. The 9 letters of the word HAPPINESS are arranged in random order in a line. Find the probability that the 3 vowels (A, E, I) are not all next to each other.
  3. Find the number of different selections of 4 letters from the 9 letters of the word HAPPINESS which contain no Ps and either one or two Ss.
OCR Further Statistics 2019 June Q3
6 marks Challenging +1.2
3 Six red counters and four blue counters are arranged in a straight line in a random order.
Find the probability that
  1. no blue counter has fewer than two red counters between it and the nearest other blue counter,
  2. no two blue counters are next to one another.
OCR Further Statistics 2020 November Q5
11 marks Challenging +1.2
26 cards are each labelled with a different letter of the alphabet, A to Z. The letters A, E, I, O and U are vowels.
  1. Five cards are selected at random without replacement. Determine the probability that the letters on at least three of the cards are vowels. [4]
  2. All 26 cards are arranged in a line, in random order.
    1. Show that the probability that all the vowels are next to one another is \(\frac{1}{2990}\). [3]
    2. Determine the probability that three of the vowels are next to each other, and the other two vowels are next to each other, but the five vowels are not all next to each other. [4]
SPS SPS ASFM 2020 May Q11
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]
SPS SPS FM 2023 February Q6
7 marks Standard +0.3
  1. The members of a team stand in a random order in a straight line for a photograph. There are four men and six women. 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]
OCR Further Statistics 2021 June Q3
11 marks Challenging +1.2
26 cards are each labelled with a different letter of the alphabet, A to Z. The letters A, E, I, O and U are vowels.
  1. Five cards are selected at random without replacement. Determine the probability that the letters on at least three of the cards are vowels. [4]
  2. All 26 cards are arranged in a line, in random order.
    1. Show that the probability that all the vowels are next to one another is \(\frac{1}{2990}\). [3]
    2. Determine the probability that three of the vowels are next to each other, and the other two vowels are next to each other, but the five vowels are not all next to each other. [4]