| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2009 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Permutations & Arrangements |
| Type | Correct ordering probability |
| Difficulty | Moderate -0.8 This is a straightforward combinations and probability question requiring basic counting principles. Part (i) is a direct application of C(8,3), part (ii) uses complementary counting or conditional probability with C(7,2)/C(8,3), and part (iii) applies permutations with 3!/(8×7×6). All techniques are standard S1 material with no conceptual challenges or novel problem-solving required. |
| Spec | 5.01a Permutations and combinations: evaluate probabilities5.01b Selection/arrangement: probability problems |
### Part i
**Answer:** $^nC_3 = 56$
**Marks:** M1, A1 2
### Part ii
**Answer:** $^nC_2$ or or $^nP_3/^nP_3$ $= \frac{1}{8}$ not from incorrect
**Marks:** M1, A1 3
**Guidance:** $^nC_1 + ^nC_1^nC_1$ or 21 or 8×7×6 or $\frac{1}{8} × \frac{1}{7} × \frac{1}{6}$ or $\frac{1}{8} × 3$ only or $\frac{1}{8} + \frac{1}{8} × \frac{1}{7} + \frac{1}{8} × \frac{1}{7} × \frac{1}{6}$ $= \frac{1}{8}$
$^nC_1 + ^nC_1^nC_1$ or 21 or 8×7×6 or $\frac{1}{8} × \frac{1}{7} × \frac{1}{6}$ (M1). indep, dep ans < 1 (A1 3)
### Part iii
**Answer:** $^8P_3$ or 8×7×6 or $^nC_1 × ^nC_1^nC_1$ or 336
**Marks:** M1, M1, A1 3
**Guidance:** $\frac{1}{8} × ^8P_3$ only = $\frac{1}{336}$ or 0.00298 (3 sf) (M1 A1 3). $\frac{1}{8} × \frac{1}{7} × \frac{1}{6}$ only M2. If × or ÷: M1 ($\frac{1}{8}$) M1
---Three letters are selected at random from the 8 letters of the word COMPUTER, without regard to order.
\begin{enumerate}[label=(\roman*)]
\item Find the number of possible selections of 3 letters. [2]
\item Find the probability that the letter P is included in the selection. [3]
\end{enumerate}
Three letters are now selected at random, one at a time, from the 8 letters of the word COMPUTER, and are placed in order in a line.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{2}
\item Find the probability that the 3 letters form the word TOP. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR S1 2009 Q7 [8]}}