OCR MEI S1 2011 January — Question 3 6 marks

Exam BoardOCR MEI
ModuleS1 (Statistics 1)
Year2011
SessionJanuary
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPermutations & Arrangements
TypeSelection with type constraints
DifficultyModerate -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.
Spec5.01a 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.
  1. In how many different ways can the three men be selected? [2]
  2. In how many different ways can the whole committee be selected? [2]
  3. 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]

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]}}