LEARN · EXPLAIN · REVISE

Choose an unordered committee of 3 from m people.

Read the idea, work independently, then explain what changed.

TOPIC 01

Counting principles: mixed review

A mixed assessment: identify the method, justify it and revise your reasoning.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Foundation#Your turn

m=15

Counts use nonnegative integer sizes; decide whether labels, order and rotations distinguish outcomes.

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Decide whether choices are alternative cases or successive stages, then check overlap.

Hint 2

Use this intermediate relation.

C_m^3=P_m^3/3!

Worked solution

Decide whether choices are alternative cases or successive stages, then check overlap.
Apply the stated relation and retain its conditions.
$N=15(14)(13)/6=455$
Each committee was counted in six possible orders.

The requested value is 455.

Checks and common pitfalls: Each committee was counted in six possible orders.

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

Teacher preparation and assessment