A-LevelMathematicsProbability and statistics9709/53 · Oct/Nov 2020 · Q57 Marks

The 8 letters in the word RESERVED are arranged in a random order.

(a)Find the probability that the arrangement has V as the first letter and E as the last letter.[3]
(b)Find the probability that the arrangement has both Rs together given that all three Es are together.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

[B1] Correct unsimplified expression for total number of ways
[B1] 6!/(2x2!) alone or as numerator in an attempt to find the number of ways with V and E in correct positions. No x,±
[B1 FT] Final answer from their 6!/(2x2!) divided by their total number of ways
[B1] Alone or as numerator of probability to represent the number of ways with Rs and Es together, no ×, +, -
[B1] Alone or as denominator of probability to represent the number of ways with Es together, no ×, + or -
[M1] (their 5!)/(their 6!/2!) seen
[A1] OE

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 7 marks.
Source: A-Level Mathematics, Oct/Nov 2020 Paper 5 Variant 3, question 5.

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