## Questions and Answers

The formula for evaluating combinations is n objects taken r at a time = n! / (r! * (n-r)!) is incorrect.

False

In Example 1, the number of groups of 4 that can be formed from 10 people is 120.

False

In Example 2, the number of ways 5 people can shake hands is 10.

True

In Example 3, the total ways of choosing a committee of 2 boys and 3 girls from 8 boys and 4 girls is 96.

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In Example 4, the total groups that can be formed by choosing a group of 5 students from 6 boys and 8 girls with at least 4 boys is 126.

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How many groups of 3 can be formed from 9 people?

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In how many ways can 4 students be selected from a group of 7 students?

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If there are 6 books on a shelf, how many ways can 2 books be selected?

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From a group of 12 athletes, how many different relay teams of 4 athletes can be formed?

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If there are 5 colors of paint, how many different pairs of colors can be chosen?

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## Study Notes

- Combination refers to selecting from a set where the order is not important.
- Formula for evaluating combinations: n objects taken r at a time = n! / ((n-r)! * r!)
- Example 1: How many groups of 4 can be formed from 10 people? Solution: 210 groups.
- Example 2: In how many ways can 5 people shake hands? Solution: 10 ways.
- Example 3: Choosing a committee of 2 boys and 3 girls from 8 boys and 4 girls. Total ways: 112.
- Example 4: Choosing a group of 5 students from 6 boys and 8 girls with at least 4 boys. Total groups that can be formed: 126.

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## Description

Test your knowledge on combinations, a concept that involves selecting objects from a set where the order is not important. Practice calculating the number of ways groups can be formed or members selected with different conditions.