Permutations and Combinations  Counting  Infinity Learn  Summary and Q&A
TL;DR
Learn the key rules of counting to understand permutations and combinations, making problemsolving easier.
Key Insights
 🔄 The understanding of counting principles is crucial for mastering permutations and combinations.
 📏 The 'OR' rule represents addition, while the 'AND' rule represents multiplication in counting techniques.
 👻 Counting techniques can be applied to various scenarios, allowing for the calculation of different combinations and permutations.
 🔄 Visual representations, such as the example of counting circles in a grid, can simplify counting and understanding permutations and combinations.
 🧑🎓 Many students find permutations and combinations challenging, but with a solid understanding of counting principles, it becomes a manageable topic.
 🔄 Formulae for permutations and combinations are useful but not as important as understanding counting principles.
 👻 Developing counting skills allows for efficient problemsolving in permutations and combinations.
Transcript
The formula for N C R is 'N factorial, divided by R' factorial times 'N minus R' factorial. What is this? This is the formula for combinations, but it is not the best way to understand it ! And what is NPR. It's N factorial over 'N minus R' factorial. And this again, is not the best way to understand permutations! In many books, and videos you woul... Read More
Questions & Answers
Q: What is the formula for calculating permutations and combinations?
The formula for permutations is N! / (NR)! while combinations use N! / (R!(NR)!). However, understanding counting principles is more important than relying solely on these formulas.
Q: How do counting techniques relate to permutations and combinations?
Counting techniques, such as understanding 'OR' and 'AND' principles, are essential to solving permutations and combinations problems. 'OR' represents addition while 'AND' represents multiplication.
Q: How can counting principles be applied to simple scenarios?
Counting principles can be applied to various scenarios. For example, if you have 3 pens and 2 markers, you can count the total number of ways to select any one item as 3 (pens) + 2 (markers) = 5.
Q: How can counting principles be used to determine the ways to select one pen and one marker?
To calculate the ways to select one pen and one marker, you multiply the number of ways to select a pen (3) with the number of ways to select a marker (2), resulting in 3 (pens) x 2 (markers) = 6.
Summary & Key Takeaways

Understanding permutations and combinations requires a solid grasp of counting techniques.

Permutations can be calculated using the formula N! / (NR)! while combinations use N! / (R!(NR)!).

The key to mastering permutations and combinations is to understand the rules of counting, which involve addition (OR) and multiplication (AND) principles.