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Questions and Answers
In a combination, what does the formula n! / ((n-r)! * r!) represent?
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?
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?
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?
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?
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What is the difference between a permutation and a combination?
What is the difference between a permutation and a combination?
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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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