permutations and combinations

The Permutations and Combinations category is often called Combinatorics, which is the branch of mathematics dealing with permutations & combinations. It begins with the Fundamental Counting Principle; the basic principle of this unit.

Permutations (arrangements where order is important) are covered in great detail. There are linear permutations (arrangements in a straight line), permutations with no restrictions, with restricted objects, with adjacent objects, and with repetitions. Circular and Ring permutations are also covered in this category.

The next topic is combinations (selections where order is not important). Questions are done using coins, committees, playing cards, polygons, etc.

Pascal's Triangle is then introduced which leads into Pathways.
The category ends with the Binomial Theorem, expanding (a+b)ⁿ. Here the connection is made between expanding a binomial & using combinations.

Lessons in the permutations and combinations category:

• 500 The Fundamental Counting Principle
• 505 Factorial Notation & Linear Permutations
• 510 Linear Permutations with Restrictions
• 515 Circular & Ring Permutations
• 520 Combinations Part I
• 525 Combinations Part II
• 530 Pascal's Triangle and Pathways
• 535 The Binomial theorem