CAIE S1 2015 June — Question 6 9 marks

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2015
SessionJune
Marks9
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPermutations & Arrangements
TypeArrangements with grouped categories
DifficultyModerate -0.8 This is a straightforward permutations and combinations question testing standard techniques. Part (a)(i) requires arranging 5 remaining letters with repetitions (3 A's) after fixing positions—a direct application of n!/r! formula. Part (a)(ii) uses the 'treat as one unit' method for adjacent letters. Part (b) is a basic complementary counting problem with combinations. All parts are textbook exercises requiring recall of standard methods with minimal problem-solving, making this easier than average for A-level.
Spec5.01a Permutations and combinations: evaluate probabilities5.01b Selection/arrangement: probability problems

  1. Find the number of different ways the 7 letters of the word BANANAS can be arranged
    1. if the first letter is N and the last letter is B, [3]
    2. if all the letters A are next to each other. [3]
  2. Find the number of ways of selecting a group of 9 people from 14 if two particular people cannot both be in the group together. [3]

\begin{enumerate}[label=(\alph*)]
\item Find the number of different ways the 7 letters of the word BANANAS can be arranged
\begin{enumerate}[label=(\roman*)]
\item if the first letter is N and the last letter is B, [3]
\item if all the letters A are next to each other. [3]
\end{enumerate}

\item Find the number of ways of selecting a group of 9 people from 14 if two particular people cannot both be in the group together. [3]
\end{enumerate}

\hfill \mbox{\textit{CAIE S1 2015 Q6 [9]}}