| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2005 |
| Session | January |
| Marks | 5 |
| 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 combinations with no complications. Part (i) requires calculating C(12,8) and part (ii) requires C(12,8) × C(11,7). Both are direct recall of the basic combination formula with simple multiplication—no problem-solving insight needed, making it easier than average. |
| Spec | 5.01a Permutations and combinations: evaluate probabilities5.01b Selection/arrangement: probability problems |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\dbinom{12}{8}\) ways of choosing forwards \(= 495\) | M1, A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\dbinom{12}{8} \times \dbinom{11}{7}\) ways of choosing team | M1, M1 | Product with (i); backs |
| \(= 495 \times 330 = 163350\) | A1 | cao |
## Question 5:
### Part (i)
| Answer | Mark | Guidance |
|--------|------|----------|
| $\dbinom{12}{8}$ ways of choosing forwards $= 495$ | M1, A1 | |
### Part (ii)
| Answer | Mark | Guidance |
|--------|------|----------|
| $\dbinom{12}{8} \times \dbinom{11}{7}$ ways of choosing team | M1, M1 | Product with (i); backs |
| $= 495 \times 330 = 163350$ | A1 | cao |
---5 A rugby union team consists of 15 players made up of 8 forwards and 7 backs. A manager has to select his team from a squad of 12 forwards and 11 backs.\\
(i) In how many ways can the manager select the forwards?\\
(ii) In how many ways can the manager select the team?
\hfill \mbox{\textit{OCR MEI S1 2005 Q5 [5]}}