﻿ Tree Diagrams

Readings for Session 9 – (Continued)

Tree Diagram

A tree diagram is another way to illustrate multiplication to figure out how many ways something can happen. It is useful in problems where several choices or stages follow one after another.  Each choice or stage is represented by a branching.  The total number of end-branches of the tree diagram shows us all the different ways the choices or stages can happen..

Example:  A coin is tossed three times and H (heads) or T (tails) is recorded for each toss. How many different outcomes are possible?

Where three coins are tossed there are eight possible distinct outcomes.
Note that the order of the outcomes is important.

The above tree diagram does not seem to match the repeated addition concept for multiplication though it is possible to interpret it as repeated addition. How would you illustrate the problem as repeated addition?   The problem does motivate another way of looking at multiplication. Since the order is important in the tree diagram, the set of solutions in the above problem is a set of ordered triplets; that is, HHT is not the same as HTH or THH even though all three have two heads and one tail. This motivates the next method which we call a Cartesian Product.