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A-LevelMathematicsProbability and statistics9709/51 · May/June 2023 · Q36 Marks

Find the number of different arrangements of the 8 letters in the word COCOONED.

  1. (a)Find the number of different arrangements of the 8 letters in the word COCOONED.[1]
  2. (b)Find the number of different arrangements of the 8 letters in the word COCOONED in which the first letter is O and the last letter is N.[2]
  3. (c)Find the probability that a randomly chosen arrangement of the 8 letters in the word COCOONED has all three Os together given that the two Cs are next to each other.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

  1. [B1]
  2. [M1] 6! / (2! f!) , ; f = 1, 2, 3.
  3. [A1]
  4. [M1] 5! / g a positive integer, g ≠ 3360, 1. Condone numerator of 5! / (3360g).
  5. [M1] h / 7! or h / 8!, where h is a positive integer. Condone division by 3360 in denominator.
  6. [A1] 0.1428571... to at least 3SF. If M0 scored SC B1 for 1/7 WWW.

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About this question

Topic
Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source
A-Level Mathematics, May/June 2023 Paper 5 Variant 1, question 3.

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