| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2014 |
| Session | June |
| Marks | 7 |
| Topic | Combinations & Selection |
| Type | Basic committee/group selection |
| Difficulty | Moderate -0.8 This is a straightforward combinations and probability question testing basic counting principles. Part (i) is a direct application of C(15,4), part (ii) requires recognizing 15^4 arrangements, and part (iii) involves computing a simple probability ratio. All parts are standard textbook exercises requiring only recall of formulas with minimal problem-solving, making it easier than average for A-level. |
| Spec | 5.01b Selection/arrangement: probability problems |
| Answer | Marks | Guidance |
|---|---|---|
| (i) Recognise combination problem. | M1 A1 | c.a.o. |
| \({}^{15}C_5 = \frac{15!}{11!4!} = 1365\) | ||
| (ii) Recognise implication of "no restrictions". | M1 A1 | c.a.o. |
| \(15^4 = 50625\) | ||
| (iii) \(\frac{15 \times 14 \times 13 \times 12}{15^4} = \frac{32760}{50625} = \frac{728}{1125} = 0.647(11...)\) | M1 M1 A1 | Correct numerator. Correct denominator; ft (ii). c.a.o. [3] |
**(i)** Recognise combination problem. | M1 A1 | c.a.o.
${}^{15}C_5 = \frac{15!}{11!4!} = 1365$ |
**(ii)** Recognise implication of "no restrictions". | M1 A1 | c.a.o.
$15^4 = 50625$ |
**(iii)** $\frac{15 \times 14 \times 13 \times 12}{15^4} = \frac{32760}{50625} = \frac{728}{1125} = 0.647(11...)$ | M1 M1 A1 | Correct numerator. Correct denominator; ft (ii). c.a.o. [3]There are 15 students enrolled in a Maths club.
\begin{enumerate}[label=(\roman*)]
\item In how many ways is it possible to choose 4 of the students to take part in a competition? [2]
\end{enumerate}
There are 4 different medals to be allocated, at random, to the students in the Maths club.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item If there are no restrictions about how many medals a student may receive, in how many ways can the medals be allocated? [2]
\item Find the probability that no student receives more than one medal. [3]
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2014 Q5 [7]}}