Unit 6

Permutations, Combinations, and The Binomial Theorem

Introduction


Lesson 6.1: Permutations and Combinations

Since you were little, you have been counting things. Perhaps as a small toddler, you learned to count to ten by counting your fingers or toes. Have you ever wondered how many ways you could count your fingers? What if you had to count your thumbs first, and then the pinkies next?

In this unit, you will learn about counting. And you thought you learned everything you ever needed to know about counting in kindergarten!

In Lesson 6.1, you will


  • use the fundamental counting principle to solve counting problems,
  • determine the number of permutations of «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»n«/mi»«/mstyle»«/math» elements taken «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»r«/mi»«/mstyle»«/math» at a time,
  • solve counting problems when two or more elements are the same,
  • solve equations involving permutation notation,
  • determine the number of combinations of «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»n«/mi»«/mstyle»«/math» elements taken «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»r«/mi»«/mstyle»«/math» at a time, and
  • solve equations using combination notation.

Coming into this Lesson, you should have


  • well-developed algebra skills, and
  • the ability to factor and expand expressions.