Arrange four distinct girls and three distinct boys in a row with no adjacent boys.

01 / Standard#Your turn

Official paper · jm01-2025 · I.7 · PDF 2

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Arrange the girls first.

Hint 2

Choose three of the five gaps for the boys.

Worked solution

Four girls create five gaps including the two ends.
$4!\binom53$
Arrange the three different boys in the selected gaps.
$N=4!\binom53\,3!=24\cdot10\cdot6=1440$

C: 1440.

Checks and common pitfalls: The two end gaps are allowed and must be counted.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Four girls create five gaps including the two ends.
$4!\binom53$
Arrange the three different boys in the selected gaps.
$N=4!\binom53\,3!=24\cdot10\cdot6=1440$

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

2025 JM01