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Worked solution

Select three of five people without assigning roles

Find the number of ways to select 3 of the 5 people to form a community.

CJC · Lecture · Self-Practice 2

Count unordered selections

The source asks for a selection of 3 people, without roles. Hence the number is (53)=5!/(3!2!)=10\binom53=5!/(3!2!)=10, matching the printed answer 10.

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Common mistakes

Selecting three people is not arranging them into three ordered positions.

Read the hint