Question
Scenario
Combination or Permutation?
Correct?
A team of 8 basketball players needs to choose a captain
and a co-captain.
Math Input:
Math Input: ❌
The batting order for seven players on a 12 person team.
Math Input:
Math Input: ❌
A team of 17 softball players needs to choose three
players to refill the water cooler.
Math Input:
Math Input: ❌
A group of 45 people are going to run a race. The top
three finishers will win a gold, silver or bronze medal,
depending on what place they finish.
Math Input:
Math Input: ❌
Suppose you find 7 articles related to the topic of your research paper. In how many ways can you choose 5 articles to read?
Math Input:
Math Input: ❌
How many three person committees can be chosen from a group of six people?
Math Input:
Combination or Permutation?
Correct?
A team of 8 basketball players needs to choose a captain
and a co-captain.
Math Input:
Math Input: ❌
The batting order for seven players on a 12 person team.
Math Input:
Math Input: ❌
A team of 17 softball players needs to choose three
players to refill the water cooler.
Math Input:
Math Input: ❌
A group of 45 people are going to run a race. The top
three finishers will win a gold, silver or bronze medal,
depending on what place they finish.
Math Input:
Math Input: ❌
Suppose you find 7 articles related to the topic of your research paper. In how many ways can you choose 5 articles to read?
Math Input:
Math Input: ❌
How many three person committees can be chosen from a group of six people?
Math Input:
Answers
GPT-4o mini
Let's analyze each scenario to determine whether it involves combinations or permutations:
1. **A team of 8 basketball players needs to choose a captain and a co-captain.**
- **Permutation:** Since the order matters (captain vs. co-captain), this is a permutation.
2. **The batting order for seven players on a 12 person team.**
- **Permutation:** The order of players matters in a batting lineup, so this is a permutation.
3. **A team of 17 softball players needs to choose three players to refill the water cooler.**
- **Combination:** Since the order in which the players are chosen does not matter, this is a combination.
4. **A group of 45 people are going to run a race. The top three finishers will win a gold, silver, or bronze medal, depending on what place they finish.**
- **Permutation:** The order matters because the finishers receive different medals based on their placement, so this is a permutation.
5. **Suppose you find 7 articles related to the topic of your research paper. In how many ways can you choose 5 articles to read?**
- **Combination:** Since the order in which the articles are read does not matter, this is a combination.
6. **How many three-person committees can be chosen from a group of six people?**
- **Combination:** Since the order does not matter in a committee, this is a combination.
To summarize:
1. **Permutation**
2. **Permutation**
3. **Combination**
4. **Permutation**
5. **Combination**
6. **Combination**
1. **A team of 8 basketball players needs to choose a captain and a co-captain.**
- **Permutation:** Since the order matters (captain vs. co-captain), this is a permutation.
2. **The batting order for seven players on a 12 person team.**
- **Permutation:** The order of players matters in a batting lineup, so this is a permutation.
3. **A team of 17 softball players needs to choose three players to refill the water cooler.**
- **Combination:** Since the order in which the players are chosen does not matter, this is a combination.
4. **A group of 45 people are going to run a race. The top three finishers will win a gold, silver, or bronze medal, depending on what place they finish.**
- **Permutation:** The order matters because the finishers receive different medals based on their placement, so this is a permutation.
5. **Suppose you find 7 articles related to the topic of your research paper. In how many ways can you choose 5 articles to read?**
- **Combination:** Since the order in which the articles are read does not matter, this is a combination.
6. **How many three-person committees can be chosen from a group of six people?**
- **Combination:** Since the order does not matter in a committee, this is a combination.
To summarize:
1. **Permutation**
2. **Permutation**
3. **Combination**
4. **Permutation**
5. **Combination**
6. **Combination**