| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2023 |
| Session | January |
| Marks | 7 |
| Topic | Combinations & Selection |
| Type | Selection from categorized items |
| Difficulty | Standard +0.3 This is a straightforward combinatorics problem requiring calculation of combinations C(5,3)×C(10,4) and then applying basic probability with careful case enumeration for part (b). While it requires systematic counting across cases (white A only, grey A only), the techniques are standard A-level Further Maths content with no novel insight needed. Slightly easier than average due to clear structure and routine application of combination formulas. |
| Spec | 5.01a Permutations and combinations: evaluate probabilities |
The diagram below shows 5 white cards and 10 grey cards, each with a letter printed on it.
\includegraphics{figure_6}
From these cards, 3 white cards and 4 grey cards are selected at random \textbf{without} regard to order.
\begin{enumerate}[label=(\alph*)]
\item How many selections of seven cards are possible? [3]
\item Find the probability that the seven cards include exactly one card showing the letter A. [4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2023 Q6 [7]}}