L6.1 A2 Permutations - Part 1
Completion requirements
Unit 6
Permutations, Combinations, and The Binomial Theorem
Read
Part 6A corresponds to section 11.1, starting on page 516 of your Pre-Calculus 12 textbook.
The Fundamental Counting Principle
The fundamental counting principle is not as complicated as it sounds.Fundamental means ‘basic’.
Counting means just that – a way to count items or events.
Principle means idea or method.
Using the fundamental counting principle involves using a method of counting events that could occur. It is often used as a chain of events occurs, where various choices are available.
A menu offers the following selections, and the customer chooses one from each category.
In how many ways can a meal be selected?
- Steak, chicken, or fish.
- A choice of vegetable: carrots or peas.
- A choice of potatoes or rice.
In how many ways can a meal be selected?
A diagram may be useful.
Often, a tree diagram is used to count the number of ways of putting events together.
To interpret this diagram, read the different pathways from left to right. So, the first possibility is steak, carrots, and potatoes. The second possibility is steak, carrots, and rice. The third possibility is steak, peas, and potatoes, and so on.
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 put a meal together from the given choices.
Often, a tree diagram is used to count the number of ways of putting events together.
To interpret this diagram, read the different pathways from left to right. So, the first possibility is steak, carrots, and potatoes. The second possibility is steak, carrots, and rice. The third possibility is steak, peas, and potatoes, and so on.
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 put a meal together from the given choices.
