A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2017 · Q610 Marks

A village hall has seats for 40 people, consisting of 8 rows with 5 seats in each row. Mary, Ahmad, Wayne, Elsie and John are the first to arrive in the village hall and no seats are taken before they arrive. How many possible arrangements are there of seating Mary, Ahmad, Wayne, Elsie and John assuming there are no restrictions?

(a)(i)A village hall has seats for 40 people, consisting of 8 rows with 5 seats in each row. Mary, Ahmad, Wayne, Elsie and John are the first to arrive in the village hall and no seats are taken before they arrive. How many possible arrangements are there of seating Mary, Ahmad, Wayne, Elsie and John assuming there are no restrictions?[2]
(a)(ii)How many possible arrangements are there of seating Mary, Ahmad, Wayne, Elsie and John if Mary and Ahmad sit together in the front row and the other three sit together in one of the other rows?[4]
(b)In how many ways can a team of 4 people be chosen from 10 people if 2 of the people, Ross and Lionel, refuse to be in the team together?[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

[1] (a)(i) ⁴⁰P₅ or ⁴⁰P₅ oe seen, can be mult by k ≥ 1
[1] (a)(i) = 78 960 960
[1] (a)(ii) 3! seen mult by k≥1
[1] (a)(ii) mult by 7
[1] (a)(ii) attempt at front row arrangements and multiplying by the 7 other rows arrangements, need not be correct
[1] (a)(ii) Total 126×8 = 1008
[1] (b) Considering no restrictions with subtraction (¹⁰C₄ –)
[1] (b) Considering both in team (⁸C₂)
[1] (b) Subtraction operation
[1] (b) 182 ways

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