| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Permutations & Arrangements |
| Type | Selection with type constraints |
| Difficulty | Moderate -0.8 This is a straightforward probability question using basic counting principles. Part (a) requires calculating complementary probability with ordered selections, part (b) is direct counting of favorable outcomes, and part (c) uses the complement or case-by-case counting. All parts involve routine application of permutations with no conceptual challenges beyond recognizing ordered vs unordered arrangements. |
| Spec | 5.01a Permutations and combinations: evaluate probabilities |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{11}{10} \times \frac{10}{13} \times \frac{n}{14} = \frac{33}{112}\) or \(0.295\) (3sf) | M2 A1 | |
| \(\frac{5}{16} \times \frac{11}{13} \times \frac{4}{14} = \frac{11}{168}\) or \(0.0655\) (3sf) | M2 A1 | |
| \(3 \times \frac{5}{16} \times \frac{11}{13} \times \frac{10}{14} = \frac{55}{112}\) or \(0.491\) (3sf) | M3 A1 | (10) |
$\frac{11}{10} \times \frac{10}{13} \times \frac{n}{14} = \frac{33}{112}$ or $0.295$ (3sf) | M2 A1 |
$\frac{5}{16} \times \frac{11}{13} \times \frac{4}{14} = \frac{11}{168}$ or $0.0655$ (3sf) | M2 A1 |
$3 \times \frac{5}{16} \times \frac{11}{13} \times \frac{10}{14} = \frac{55}{112}$ or $0.491$ (3sf) | M3 A1 | (10)\begin{enumerate}
\item There are 16 competitors in a table-tennis competition, 5 of which come from Racknor Comprehensive School. Prizes are awarded to the competitors finishing in each of first, second and third place.
\end{enumerate}
Assuming that all the competitors have an equal chance of success, find the probability that the students from Racknor Comprehensive\\
(a) win no prizes,\\
(b) win the $1 ^ { \text {st } }$ and $3 ^ { \text {rd } }$ place prizes but not the $2 ^ { \text {nd } }$ place prize,\\
(c) win exactly one of the prizes.\\
\hfill \mbox{\textit{Edexcel S1 Q1 [10]}}