| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2020 |
| Session | Specimen |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Combinations & Selection |
| Type | Arrangements in multiple rows/groups |
| Difficulty | Standard +0.3 This is a straightforward two-part combinations question requiring basic selection (choosing 4 from 8 friends for one taxi) and then simple arrangements with a constraint (arranging people in seats with one person fixed). Both parts use standard formulas (combinations and permutations) with minimal problem-solving required, making it slightly easier than average for A-level. |
| Spec | 5.01a Permutations and combinations: evaluate probabilities |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| [Two in same taxi:] \(^6C_2 \times\, ^4C_4 \times 2\) or \(^6C_2 +\, ^6C_4\) | M1 | \(^6C_4\) or \(^6C_2\) OE seen anywhere |
| M1 | 'something' \(\times 2\) only or adding 2 equal terms | |
| \(= 30\) | A1 | |
| Total: 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| [Mark, Jon and Sarah in taxi P:] \((^5C_1 \times 2 \times 2) \times\, ^4P_4\) | M1 | \(^5P_1\), \(^5C_1\) or 5 seen anywhere |
| M1 | Multiply by 2 or 4 OE | |
| M1 | Multiply by \(^4P_4\) OE, e.g. \(4!\) or \(4 \times\, ^3P_3\) or can be part of \(5!\) | |
| \(= 480\) | A1 | |
| Total: 4 |
## Question 6:
**Part 6(a):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| [Two in same taxi:] $^6C_2 \times\, ^4C_4 \times 2$ or $^6C_2 +\, ^6C_4$ | M1 | $^6C_4$ or $^6C_2$ OE seen anywhere |
| | M1 | 'something' $\times 2$ only or adding 2 equal terms |
| $= 30$ | A1 | |
| **Total: 3** | | |
**Part 6(b):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| [Mark, Jon and Sarah in taxi P:] $(^5C_1 \times 2 \times 2) \times\, ^4P_4$ | M1 | $^5P_1$, $^5C_1$ or 5 seen anywhere |
| | M1 | Multiply by 2 or 4 OE |
| | M1 | Multiply by $^4P_4$ OE, e.g. $4!$ or $4 \times\, ^3P_3$ or can be part of $5!$ |
| $= 480$ | A1 | |
| **Total: 4** | | |
---6 A group of 8 friends travels to the airport in two taxis, $P$ and $Q$. Each taxi can take 4 passengers.\\
(a) The 8 friends divide themselves into two groups of 4, one group for taxi $P$ and one group for taxi $Q$, with Jon and Sarah travelling in the same taxi.
Find the number of different ways in which this can be done.\\
\includegraphics[max width=\textwidth, alt={}, center]{adcf5ddd-5d49-45d1-b1fb-83d702c61082-11_272_456_242_461}\\
\includegraphics[max width=\textwidth, alt={}, center]{adcf5ddd-5d49-45d1-b1fb-83d702c61082-11_281_455_233_1151}
Each taxi can take 1 passenger in the front and 3 passengers in the back (see diagram). Mark sits in the front of taxi $P$ and Jon and Sarah sit in the back of taxi $P$ next to each other.\\
(b) Find the number of different seating arrangements that are now possible for the 8 friends.\\
\hfill \mbox{\textit{CAIE S1 2020 Q6 [7]}}