Count five-person committees from six boys and four girls, with at least three boys and one girl.

01 / Standard#Your turn

Official paper · jm01-2026 · I.10 · PDF 3

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

List the possible numbers of boys and girls.

Hint 2

The cases are (3,2) and (4,1).

Worked solution

Choose the members independently within each case.
$N_{3,2}=\binom63\binom42=120,\quad N_{4,1}=\binom64\binom41=60$
The two cases are disjoint, so add.
$N=120+60=180$

A: 180 committees.

Checks and common pitfalls: A committee has no ordering; permutations would overcount.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Choose the members independently within each case.
$N_{3,2}=\binom63\binom42=120,\quad N_{4,1}=\binom64\binom41=60$
The two cases are disjoint, so add.
$N=120+60=180$

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

2026 JM01