| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2011 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Permutations & Arrangements |
| Type | Selection with type constraints |
| Difficulty | Moderate -0.8 This is a straightforward combinations question testing basic counting principles. Part (i) requires C(13,3), part (ii) requires C(13,3)×C(10,3), and part (iii) requires dividing this by C(23,6). All three parts are direct applications of the combination formula with no problem-solving insight needed, making this easier than average for A-level. |
| Spec | 5.01a Permutations and combinations: evaluate probabilities |
There are 13 men and 10 women in a running club. A committee of 3 men and 3 women is to be selected.
\begin{enumerate}[label=(\roman*)]
\item In how many different ways can the three men be selected? [2]
\item In how many different ways can the whole committee be selected? [2]
\item A random sample of 6 people is selected from the running club. Find the probability that this sample consists of 3 men and 3 women. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI S1 2011 Q3 [6]}}