| Exam Board | SPS |
|---|---|
| Module | SPS FM Statistics (SPS FM Statistics) |
| Year | 2026 |
| Session | January |
| Marks | 8 |
| Topic | Permutations & Arrangements |
| Type | Arrangements with adjacency requirements |
| Difficulty | Moderate -0.8 This is a straightforward permutations question testing standard techniques: arrangements with repeated letters (dividing by 3!2! for the Ds and Is), treating adjacent items as a single unit, and basic probability with 'at least one' complementary counting. All parts use direct formula application with no problem-solving insight required, making it easier than average but not trivial due to the multi-part structure. |
| Spec | 5.01a Permutations and combinations: evaluate probabilities |
8. Each of the 7 letters in the word DIVIDED is printed on a separate card. The cards are arranged in a row.\\
\begin{enumerate}[label=(\roman*)]
\item How many different arrangements of the letters are possible?
\item In how many of these arrangements are all three Ds together?
The 7 cards are now shuffled and 2 cards are selected at random, without replacement.
\item Find the probability that at least one of these 2 cards has D printed on it.\\[0pt]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Statistics 2026 Q8 [8]}}