CAIE S1 2010 November — Question 6 10 marks

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2010
SessionNovember
Marks10
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Mark schemeDownload PDF ↗
TopicPermutations & Arrangements
TypeSeating arrangements with constraints
DifficultyStandard +0.3 This is a standard permutations question with constraints that are straightforward to handle systematically. Part (i) is basic P(14,12), part (ii) requires careful counting but uses standard techniques (placing groups with restrictions), and part (iii) involves simple probability calculation. While multi-part and requiring organization, it demands no novel insight—just methodical application of counting principles taught in S1.
Spec5.01a Permutations and combinations: evaluate probabilities
6 \includegraphics[max width=\textwidth, alt={}, center]{ec425eaf-8afc-4671-9ef3-ba2477b884ef-4_387_899_255_623} A small aeroplane has 14 seats for passengers. The seats are arranged in 4 rows of 3 seats and a back row of 2 seats (see diagram). 12 passengers board the aeroplane.
  1. How many possible seating arrangements are there for the 12 passengers? Give your answer correct to 3 significant figures. These 12 passengers consist of 2 married couples (Mr and Mrs Lin and Mr and Mrs Brown), 5 students and 3 business people.
  2. The 3 business people sit in the front row. The 5 students each sit at a window seat. Mr and Mrs Lin sit in the same row on the same side of the aisle. Mr and Mrs Brown sit in another row on the same side of the aisle. How many possible seating arrangements are there?
  3. If, instead, the 12 passengers are seated randomly, find the probability that Mrs Lin sits directly behind a student and Mrs Brown sits in the front row.
6\\
\includegraphics[max width=\textwidth, alt={}, center]{ec425eaf-8afc-4671-9ef3-ba2477b884ef-4_387_899_255_623}

A small aeroplane has 14 seats for passengers. The seats are arranged in 4 rows of 3 seats and a back row of 2 seats (see diagram). 12 passengers board the aeroplane.\\
(i) How many possible seating arrangements are there for the 12 passengers? Give your answer correct to 3 significant figures.

These 12 passengers consist of 2 married couples (Mr and Mrs Lin and Mr and Mrs Brown), 5 students and 3 business people.\\
(ii) The 3 business people sit in the front row. The 5 students each sit at a window seat. Mr and Mrs Lin sit in the same row on the same side of the aisle. Mr and Mrs Brown sit in another row on the same side of the aisle. How many possible seating arrangements are there?\\
(iii) If, instead, the 12 passengers are seated randomly, find the probability that Mrs Lin sits directly behind a student and Mrs Brown sits in the front row.

\hfill \mbox{\textit{CAIE S1 2010 Q6 [10]}}
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