Nine distinct books consist of four Chinese, two English and three mathematics books. Three are chosen uniformly without replacement. Find the probability of one of each kind.

01 / Standard#Your turn

Official paper · jm01-2021 · II.1(a) · PDF 4

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Count unordered three-book samples.

Hint 2

Choose one book independently from each category for the favourable count.

Worked solution

The total and favourable counts are combination counts.
$N=\binom93=84,\quad F=4\cdot2\cdot3=24$
Reduce the fraction.
$P=24/84=2/7$

2/7.

Checks and common pitfalls: The categories have unequal sizes; treating the three categories as equally likely draws would be wrong.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
The total and favourable counts are combination counts.
$N=\binom93=84,\quad F=4\cdot2\cdot3=24$
Reduce the fraction.
$P=24/84=2/7$

Think first. Reveal a hint when the class is ready.

2021 JM01