Unit 6

Permutations, Combinations, and The Binomial Theorem

In a simple situation, making a diagram is a helpful way to count. However, when many choices are available, the diagram will become very large and complicated. There must be an efficient mathematical way to count when given a chain of events.

The fundamental counting principle provides a mathematical way of counting.

There are three ways to choose the main meat in the meal in Example 1.

And, there are two ways to choose the vegetable in the meal.

And, there are two ways to choose the starch in the meal.

In the previous Example, we counted each choice. The word “and” is an indication to multiply.

The menu offers «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mn»3«/mn»«/mstyle»«/math» ways to choose meat and «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mn»2«/mn»«/mstyle»«/math» ways to choose a vegetable and «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mn»2«/mn»«/mstyle»«/math» ways to choose a starch.


There are «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mn»12«/mn»«/mstyle»«/math» ways to choose a meal.