| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2019 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Permutations & Arrangements |
| Type | Arrangements with couples/pairs |
| Difficulty | Moderate -0.8 Part (i) is a straightforward application of fixing two positions (2 ways to assign which man goes where) then arranging the remaining 9 people (9!). Part (ii) requires treating groups as single units (2 blocks plus 4 individuals = 6! arrangements, with internal arrangements 5! and 2!), which is a standard textbook technique for grouped permutations. Both parts involve direct application of well-practiced methods with no novel problem-solving required. |
| Spec | 5.01a Permutations and combinations: evaluate probabilities |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(9! \times 2\) | B1 | 9! seen multiplied by \(k \geqslant 1\), no addition |
| \(= 725760\) | B1 | Exact value |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Eg \((K_1K_2K_3K_4K_5)\ A\ A\ A\ (U_1U_2)\ A\) | B1 | 2! or 5! seen multiplied by \(k > 1\), no addition (arranging Us or Ks) |
| \(= 5! \times 2! \times 6!\) | B1 | 6! seen multiplied by \(k > 1\), no addition (arranging AAAAKU) |
| \(= 172800\) | B1 | Exact value |
## Question 3(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $9! \times 2$ | B1 | 9! seen multiplied by $k \geqslant 1$, no addition |
| $= 725760$ | B1 | Exact value |
---
## Question 3(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Eg $(K_1K_2K_3K_4K_5)\ A\ A\ A\ (U_1U_2)\ A$ | B1 | 2! or 5! seen multiplied by $k > 1$, no addition (arranging Us or Ks) |
| $= 5! \times 2! \times 6!$ | B1 | 6! seen multiplied by $k > 1$, no addition (arranging AAAAKU) |
| $= 172800$ | B1 | Exact value |
---3 Mr and Mrs Keene and their 5 children all go to watch a football match, together with their friends Mr and Mrs Uzuma and their 2 children. Find the number of ways in which all 11 people can line up at the entrance in each of the following cases.\\
(i) Mr Keene stands at one end of the line and Mr Uzuma stands at the other end.\\
(ii) The 5 Keene children all stand together and the Uzuma children both stand together.\\
\hfill \mbox{\textit{CAIE S1 2019 Q3 [5]}}