| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2017 |
| Session | June |
| Marks | 9 |
| Topic | Permutations & Arrangements |
| Type | Basic arrangements with repeated letters |
| Difficulty | Moderate -0.3 This is a standard permutations question with repeated letters requiring straightforward application of the formula n!/n₁!n₂!... for arrangements. Part (i) is direct calculation, part (ii) requires fixing positions then counting, and part (iii) involves treating grouped letters as a single unit. While it has multiple parts, each uses routine techniques without requiring novel insight or complex problem-solving, making it slightly easier than average. |
| Spec | 5.01a Permutations and combinations: evaluate probabilities |
**Question 4(i)**
- $\dfrac{10!}{\cdots}$ **B1**
- Reasonable attempt at denominator **M1**
- $\dfrac{10!}{3!3!2!} = 50400$ **A1** (cao)
**Question 4(ii)**
- $\dfrac{8!}{3!2!}$ **M1** (Arrangements of 'TATISTIC': $\dfrac{8!}{\cdots}$)
- Denominator correct for repeated letters **M1**
- $= 3360$ **A1** (cao)
**Question 4(iii)**
- $\dfrac{\dfrac{8!}{3!2!}}{\dfrac{10!}{3!3!2!}} = \dfrac{3360}{50400}$ **M2** (M1 Numerator; allow *their* (ii). M1 Denominator; allow *their* (i).)
- $= \dfrac{1}{15}$ **A1** (FT *their* (ii) and/or *their* (i).)
**Total: 9 marks**4 The letters of the word 'STATISTICS' are to be rearranged.\\
(i) How many distinct arrangements are there?\\
(ii) How many of the arrangements start and end with the letter S ?\\
(iii) What is the probability that, in a randomly chosen arrangement, the S's are all together?
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2017 Q4 [9]}}