2024 H2 Mathematics Paper 2 Question 6

Permutations and Combinations (P&C)

Answers

It comprise a sample as the $65$ members is a subset of the population.

Choosing a random sample means all members have a equal chance of being chosen so this leads to a sample that is free from bias.

$\frac{13}{32} .$

(a)

The $65$ form a sample because not all $27 + 45 + 18 = 90$ members replied, so the $65$ is a subset of the population $∎$

(b)

Choosing a random sample means all members have a equal chance of being chosen so this leads to a sample that is free from bias $∎$

(c)

There are 3 cases to consider:

Only in the first case the committee contains more Youth members than Senior members

\begin{aligned} P (required) \\ = \frac{(\binom{45}{3}) (\binom{27}{2}) (\binom{18}{1})}{(\binom{45}{3}) (\binom{27}{2}) (\binom{18}{1}) + (\binom{45}{3}) (\binom{27}{1}) (\binom{18}{2}) + (\binom{45}{4}) (\binom{27}{1}) (\binom{18}{1})} \\ = \frac{13}{32} ∎ \end{aligned}