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A-LevelMathematicsProbability and statistics9709/62 · Oct/Nov 2018 · Q15 Marks

How many different arrangements are there of the 11 letters in the word MISSISSIPPI?

  1. (i)How many different arrangements are there of the 11 letters in the word MISSISSIPPI?[2]
  2. (ii)Two letters are chosen at random from the 11 letters in the word MISSISSIPPI. Find the probability that these two letters are the same.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

  1. [M1] 11! / (4!xk 2xk) k a positive integer
  2. [A1] Correct final answer
  3. [B1] One of P(SS), P(PP) or P(II) correct, allow unsimplified
  4. [M1] Sum of probabilities from 3 appropriate identifiable scenarios (either by labelling or of form (4a/11b * 2c/11b * 4a/11b) where a=4 or 3, b=11 or 10, c=2 or 1)
  5. [A1] Correct final answer

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About this question

Topic
Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, Oct/Nov 2018 Paper 6 Variant 2, question 1.

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