📚 Topic Summary
Permutations and combinations are fundamental concepts in probability that help us count the number of ways events can occur. Permutations are used when the order of selection matters, while combinations are used when the order does not matter. Probability then allows us to determine the likelihood of these events.
Understanding the difference is crucial for solving probability problems correctly. Think of it this way: arranging a race (order matters, permutation) versus forming a committee (order doesn't matter, combination).
🧮 Part A: Vocabulary
Match the following terms with their definitions:
- Permutation
- Combination
- Probability
- Factorial
- Sample Space
Definitions:
- The set of all possible outcomes of an experiment.
- A selection of items where the order does not matter.
- The likelihood of an event occurring.
- The product of all positive integers less than or equal to a given number.
- An arrangement of items in a specific order.
(Match the terms with the correct definitions)
✏️ Part B: Fill in the Blanks
Complete the following paragraph using the words: permutation, combination, probability, factorial, events.
When the order of items matters, we use a __________. If the order does not matter, we use a __________. __________ is the measure of how likely __________ are to occur. The __________ of a number $n$ is written as $n!$ and means $n \times (n-1) \times (n-2) \times ... \times 1$.
🤔 Part C: Critical Thinking
Explain, in your own words, the difference between a permutation and a combination. Give a real-world example of each.