Permutations and Combinations


In this lesson of the Probability Fundamentals course, you will calculate the number of outcomes associated with various random experiments, and some powerful counting techniques that will allow us to answer questions such as:

  • What is the probability of cracking a 4-digit PIN code using the code `8362`?
  • What is the probability of cracking a 6-digit PIN code using the code `348821`?
  • What is the probability of winning the big prize in a state lottery if we use the numbers `3, 20, 37, 44, 45, 49`?

You’ll learn concepts such as rule of product, and permutations and combinations, and why they are important for solving probability problems.

Permutations and combinations are both types of groups, but the difference is that in a permutation, the order of the elements matters, while in a combination, the order does not. For example, there are 10,000 possible permutations for a 4-digit PIN code, but the code represents only one combination.

You’ll also learn about factorials, and what they mean mathematically, as well as how they relate to permutations and combinations.


  • Learn about the rule of product
  • Learn about permutations
  • Learn about combinations

Lesson Outline

  1. The Rule of Product
  2. Extended Rule of Product
  3. Example Walkthrough
  4. Permutations
  5. More About Perrmutations
  6. Permutatuin Formulas
  7. Unique Arrangements
  8. Combinations
  9. Next Steps
  10. Takeaways

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