| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2003 |
| Session | November |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Combinations & Selection |
| Type | Basic committee/group selection |
| Difficulty | Easy -1.2 This is a straightforward application of basic combinatorics formulas requiring only direct recall and substitution. Part (a) uses simple combinations C(18,6) and C(17,5), while part (b) applies basic permutations and the standard 'treat as one unit' technique. No problem-solving insight or multi-step reasoning is needed—these are textbook exercises testing formula knowledge. |
| Spec | 5.01a Permutations and combinations: evaluate probabilities5.01b Selection/arrangement: probability problems |
| Answer | Marks | Guidance |
|---|---|---|
| (a)(i) 18564 | B1 | For correct final answer |
| (a)(ii) \(_{17}C_5\) or \(6/18 \times\) their (i) or \(_{17}C_6 = 6188\) | M1 | For using 17 and 5 as a perm or comb |
| A1 | For correct answer |
| Answer | Marks | Guidance |
|---|---|---|
| (b)(i) 40320 | B1 | For correct final answer |
| (b)(ii) \(5! \times 3! \times {}_4C_1\) \(= 2880\) | B1 | For 5!or \(_{5}P_5\) used in a prod or quotient with a term ≠ 5! |
| B1 | For 3! | |
| B1 | For \({}_{4}C_{1}\), may be implied by 4! | |
| B1 | For correct final answer |
**(a)(i)** 18564 | B1 | For correct final answer
**(a)(ii)** $_{17}C_5$ or $6/18 \times$ their (i) or $_{17}C_6 = 6188$ | M1 | For using 17 and 5 as a perm or comb
A1 | For correct answer
**2 marks total**
**(b)(i)** 40320 | B1 | For correct final answer
**(b)(ii)** $5! \times 3! \times {}_4C_1$ $= 2880$ | B1 | For 5!or $_{5}P_5$ used in a prod or quotient with a term ≠ 5!
B1 | For 3!
B1 | For ${}_{4}C_{1}$, may be implied by 4!
B1 | For correct final answer
**4 marks total**
---6
\begin{enumerate}[label=(\alph*)]
\item A collection of 18 books contains one Harry Potter book. Linda is going to choose 6 of these books to take on holiday.
\begin{enumerate}[label=(\roman*)]
\item In how many ways can she choose 6 books?
\item How many of these choices will include the Harry Potter book?
\end{enumerate}\item In how many ways can 5 boys and 3 girls stand in a straight line
\begin{enumerate}[label=(\roman*)]
\item if there are no restrictions,
\item if the boys stand next to each other?
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{CAIE S1 2003 Q6 [8]}}