Everything Maths Grade 12

CHAPTER 12. COMBINATIONS AND PERMUTATIONS 12.3

Both these methods result in 12 possible outcomes, but both these methods have a lot of repetition.

Maybe there is a smarter way to write down theresult?

Tree Diagrams EMCDE

One method of eliminating some of the repetition is to use tree diagrams. Tree diagrams are a graphical

method of listing all possible combinations of events from a random experiment.

1 2 3 654

H T H T H T THTHTH

coin

die

Figure 12.1: Example ofa tree diagram. Each possible outcome is a branch of the tree.

12.3 Notation EMCDF

Factorial Notation EMCDG

For an integer n, the notation n! (read n factorial) represents:

n× (n− 1)× (n− 2)×···× 3 × 2 × 1

with the following definition: 0! = 1.

The factorial notation will be used often in thischapter.

12.4 Fundamental Counting Principle

EMCDH

The use of lists, tables and tree diagrams is onlyfeasible for events witha few outcomes. Whenthe

number of outcomes grows, it is not practicalto list the different possibilities and the fundamental

counting principle is used.

The fundamental countingprinciple describes how to determine the total number of outcomes of a

series of events.

Suppose that two experiments take place. Thefirst experiment has n 1 possible outcomes, andthe

second has n 2 possible outcomes. Therefore, the first experiment, followed by the second experiment,