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Combinations and Selections

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Questions and Answers

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.