| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2009 |
| Session | November |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Permutations & Arrangements |
| Type | Digit arrangements forming numbers |
| Difficulty | Moderate -0.8 This is a straightforward permutations question testing standard counting techniques. Part (a)(i) is basic permutation (4! = 24), part (a)(ii) requires simple case-by-case counting with constraints (odd last digit, first digit ≥5), and part (b) uses complement counting for arrangements. All techniques are routine for A-level statistics students with no novel problem-solving required. |
| Spec | 5.01a Permutations and combinations: evaluate probabilities5.01b Selection/arrangement: probability problems |
4
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Find how many different four-digit numbers can be made using only the digits 1, 3, 5 and 6 with no digit being repeated.
\item Find how many different odd numbers greater than 500 can be made using some or all of the digits $1,3,5$ and 6 with no digit being repeated.
\end{enumerate}\item Six cards numbered 1,2,3,4,5,6 are arranged randomly in a line. Find the probability that the cards numbered 4 and 5 are not next to each other.
\end{enumerate}
\hfill \mbox{\textit{CAIE S1 2009 Q4 [8]}}