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# Combinations and Selections

Created by
@BestUranium

### In a combination, what does the formula n! / ((n-r)! * r!) represent?

• Total number of objects when order matters but repetition is not allowed
• Total number of objects when both order and repetition matter
• Total number of ways to select r objects from n objects without considering the order (correct)
• Total number of ways to arrange r objects in a specific order from n objects
• ### How many groups of 3 can be formed from 7 people using combinations?

• 28 groups
• 35 groups
• 42 groups
• 21 groups (correct)
• ### What does it mean when selecting a committee of 2 boys and 3 girls from a group of 8 boys and 4 girls?

• Order of selection matters
• Only selection of boys is considered
• There are more girls than boys in the group
• Combination is being used where order does not matter (correct)
• ### If we need to form a group of 4 students from 9 boys and 5 girls with at least 2 girls, how many groups can be formed?

<p>105 groups</p> Signup and view all the answers

### What is the difference between a permutation and a combination?

<p>Permutation considers order, while combination does not</p> Signup and view all the answers

## 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 understanding of combinations by solving problems involving selecting groups from a given set without considering the order. Explore different scenarios like forming groups, shaking hands, and selecting committees to practice applying the combination formula.

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