| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2007 |
| Session | June |
| Marks | 4 |
| 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 combination formulas (C(15,7) and C(6,3)×C(9,4)) with no problem-solving required beyond recognizing the standard setup. It's easier than average as it only tests direct recall of nCr in two simple scenarios, typical of early S1 material. |
| Spec | 5.01a Permutations and combinations: evaluate probabilities5.01b Selection/arrangement: probability problems |
| Answer | Marks |
|---|---|
| 6435 | M1 |
| A1 | |
| 2 |
| Answer | Marks | Guidance |
|---|---|---|
| \(^{12}C_3 × ^4C_1 × ^{8/}_{131} × ^9/_1s\) | M1 | Alone except allow \(÷ ^{12}C_7\) |
| Or \(^8P_3 × ^4P_1\) or \(^{8}/_1s × ^9/_1s\). Allow \(÷ ^1P_7\) | ||
| NB not \(^{8}/_1s×^9/_1s\) | ||
| 2520 | A1 | 362880 |
### Part i
$^{13}C$ or $^{187}_{m}Rn$ or similar
6435 | M1 |
| A1 |
| 2 |
### Part ii
$^{12}C_3 × ^4C_1 × ^{8/}_{131} × ^9/_1s$ | M1 | Alone except allow $÷ ^{12}C_7$
| | Or $^8P_3 × ^4P_1$ or $^{8}/_1s × ^9/_1s$. Allow $÷ ^1P_7$
| | NB not $^{8}/_1s×^9/_1s$
2520 | A1 | 362880
**Total: 4**
---3 (i) How many different teams of 7 people can be chosen, without regard to order, from a squad of 15 ?\\
(ii) The squad consists of 6 forwards and 9 defenders. How many different teams containing 3 forwards and 4 defenders can be chosen?
\hfill \mbox{\textit{OCR S1 2007 Q3 [4]}}