QQuestionMathematics
QuestionMathematics
Explain the difference between a combination and a permutation in your own words. Give examples.
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Step 1I'll solve this problem by explaining the difference between combinations and permutations with clear examples:
Step 2: Understanding Combinations
- $$r$$ is the number of items being selected
A combination is a selection of items where the order does NOT matter. When choosing items from a group, we only care about which items are selected, not the sequence in which they are selected. Example of a Combination: Imagine selecting 3 toppings for a pizza from 5 available toppings. The order of selecting these toppings is irrelevant. Choosing pepperoni, mushrooms, and olives is the same as choosing olives, pepperoni, and mushrooms. The combination formula is: Where:
Final Answer
Combinations select items without regard to order, while permutations arrange items where order is significant. The key distinction is whether the sequence matters in the selection process.
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