A-LevelMathematicsProbability and statistics9709/63 · May/June 2018 · Q710 Marks

Find the number of ways the 9 letters of the word SEVENTEEN can be arranged in each of the following cases. 5 letters are chosen from the 9 letters of the word SEVENTEEN.

(i)One of the letter Es is in the centre with 4 letters on either side.[2]
(ii)No E is next to another E.[3]
(iii)Find the number of possible selections which contain exactly 2 Es and exactly 2 Ns.[1]
(iv)Find the number of possible selections which contain at least 2 Es.[4]

Mark scheme

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

[2] M1 Mult by 8! or P8 oe (arrangements ignoring repeats)
[2] A1 Correct final answer www
[3] M1 k mult by ⁶C₄ or ⁶P₄ oe (ways to insert Es ignoring repeats), k can = 1 or k mult by 5!/2!
[3] M1 Correct unsimplified expression or 5!/2! x ⁶P₄
[3] A1 Correct answer
[1] B1 Numerical value must be stated
[4] M1 Identifying the three different scenarios of EE, EEE or EEEE
[4] A1 Total no of ways with two Es (7 or 3 + 3 + 1)
[4] A1 Total no. of ways with 3 Es (7)
[4] A1 Correct answer stated

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 10 marks.
Source: A-Level Mathematics, May/June 2018 Paper 6 Variant 3, question 7.

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