Which of the following is an example of a combination?
In mathematics, a combination is a selection of items from a set where the order of the items does not matter. A permutation is a selection of items from a set where the order of the items does matter.
To determine whether a given problem is a combination or a permutation, we can ask the following question:
- Does the order of the items matter?
If the order of the items does not matter, then the problem is a combination. If the order of the items does matter, then the problem is a permutation.
Examples of combinations
Here are some examples of combinations:
- Choosing 5 cards from a deck of 52 cards
- Choosing 3 people to represent a group of 12 people
- Choosing a combination lock code
In each of these examples, the order of the items does not matter. For example, if we choose the cards 2 of hearts, 3 of spades, and 4 of diamonds, it is the same combination as choosing the cards 4 of diamonds, 3 of spades, and 2 of hearts.
Questions related to combinations
Here are some questions that can be used to test whether a given problem is a combination:
- Can the items be rearranged in any order?
- Does the order of the items have any significance?
- Is the order of the items simply a matter of convenience?
For example, the following questions can be used to test whether the problem of choosing 5 cards from a deck of 52 cards is a combination:
- Can the cards be rearranged in any order?
- Does the order of the cards have any significance?
- Is the order of the cards simply a matter of convenience?
The answer to all of these questions is yes, so the problem of choosing 5 cards from a deck of 52 cards is a combination.
Conclusion
To determine whether a given problem is a combination or a permutation, we can ask the question:
- Does the order of the items matter?
If the answer is no, then the problem is a combination. If the answer is yes, then the problem is a permutation.
