| Exam Board | SPS |
|---|---|
| Module | SPS FM Statistics (SPS FM Statistics) |
| Year | 2021 |
| Session | June |
| Marks | 4 |
| Topic | Permutations & Arrangements |
| Type | At least/at most N letters between items |
| Difficulty | Standard +0.3 Part (i) is a standard permutations with repetition problem (9!/(3!2!2!)). Part (ii) requires complementary counting or systematic case analysis to handle the constraint about vowels, which is a step beyond routine but still a familiar A-level technique with clear structure and only 3 marks allocated. |
| Spec | 5.01a Permutations and combinations: evaluate probabilities5.01b Selection/arrangement: probability problems |
The letters of the word CHAFFINCH are written on cards.
\begin{enumerate}[label=(\roman*)]
\item In how many ways can the letters be rearranged with no restrictions. [1]
\item In how many difference ways can the letters be rearranged if the vowels are to have at least one consonant between them. [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Statistics 2021 Q3 [4]}}