| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2005 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Combinations & Selection |
| Type | Selection from categorized items |
| Difficulty | Moderate -0.8 This is a straightforward combinations question requiring direct application of C(n,r) formula with no conceptual challenges. Part (i) is trivial, part (ii) uses the multiplication principle, and part (iii) applies basic probability = favorable/total outcomes. All steps are routine calculations with no problem-solving insight needed. |
| Spec | 5.01a Permutations and combinations: evaluate probabilities5.01b Selection/arrangement: probability problems |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Number of choices \(= \binom{6}{3} = 20\) | M1 A1 | For \(\binom{6}{3}\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Number of ways \(= \binom{6}{3} \times \binom{7}{4} \times \binom{8}{5}\) | M1 M1 | Correct 3 terms; Multiplied |
| \(= 20 \times 35 \times 56 = 39200\) | A1 cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Number of ways of choosing 12 questions \(= \binom{21}{12} = 293930\) | M1 | For \(\binom{21}{12}\) |
| Probability \(= 39200/293930 = 0.133\) | M1 ft A1 cao |
## Question 4:
### Part (i)
| Answer | Mark | Guidance |
|--------|------|----------|
| Number of choices $= \binom{6}{3} = 20$ | M1 A1 | For $\binom{6}{3}$ |
### Part (ii)
| Answer | Mark | Guidance |
|--------|------|----------|
| Number of ways $= \binom{6}{3} \times \binom{7}{4} \times \binom{8}{5}$ | M1 M1 | Correct 3 terms; Multiplied |
| $= 20 \times 35 \times 56 = 39200$ | A1 cao | |
### Part (iii)
| Answer | Mark | Guidance |
|--------|------|----------|
| Number of ways of choosing 12 questions $= \binom{21}{12} = 293930$ | M1 | For $\binom{21}{12}$ |
| Probability $= 39200/293930 = 0.133$ | M1 ft A1 cao | |
---4 An examination paper consists of three sections.
\begin{itemize}
\item Section A contains 6 questions of which the candidate must answer 3
\item Section B contains 7 questions of which the candidate must answer 4
\item Section C contains 8 questions of which the candidate must answer 5\\
(i) In how many ways can a candidate choose 3 questions from Section A?\\
(ii) In how many ways can a candidate choose 3 questions from Section A, 4 from Section B and 5 from Section C?
\end{itemize}
A candidate does not read the instructions and selects 12 questions at random.\\
(iii) Find the probability that they happen to be 3 from Section A, 4 from Section B and 5 from Section C.
\hfill \mbox{\textit{OCR MEI S1 2005 Q4 [8]}}