| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2018 |
| Session | June |
| Marks | 12 |
| Topic | Combinations & Selection |
| Type | Committee with gender/category constraints |
| Difficulty | Moderate -0.3 This is a straightforward combinations question with standard constraints. Part (i) is basic C(11,6), part (ii) requires summing cases (3,4,5 women) which is routine, and part (iii) involves conditional probability with combinations but follows a standard pattern. All techniques are textbook exercises requiring no novel insight, though the multi-part structure and careful case-work place it slightly below average difficulty. |
| Spec | 5.01a Permutations and combinations: evaluate probabilities5.01b Selection/arrangement: probability problems |
**Question 6(i)**
$\binom{11}{6} = 462$ **B1**
**Question 6(ii)**
Consider all possibilities $(3W, 3M)$, $(4W, 2M)$, $(5W, 1M)$ **M1**
${}^5C_3 \times {}^6C_3,\ {}^5C_4 \times {}^6C_2,\ {}^5C_5 \times {}^6C_1$ **B2** **B1** for one correct
$281$ **A1**
**Question 6(iii)**
Number of teams with 3 women is ${}^5C_3 \times {}^6C_3 = 200$ **B1** Need not be evaluated
Number of teams with married couple is ${}^4C_2 \times {}^5C_2 = 60$ **B1** Need not be evaluated
$\frac{60}{200}$ oe **B1**
OR
$\frac{{}^4C_2}{{}^5C_3} (= 0.6)$ **B1** Or other method to give $0.6$
$\frac{{}^5C_4}{{}^6C_3} (= 0.5)$ **B1** Or other method to give $0.5$
$\frac{60}{200}$ oe **B1**6 A volleyball squad has 11 players. A volleyball team consists of 6 players.\\
(i) Find the total number of different teams that could be chosen from the squad.
The squad has 5 women and 6 men.\\
(ii) Find the total number of different teams that contain at least 3 women.
The squad includes a man and a woman who are married to one another.\\
(iii) It is given that the team chosen has exactly 3 women and all such teams are equally likely to be chosen. Calculate the probability that a team chosen includes the married couple.
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2018 Q6 [12]}}