Readings for Session 4 – (Continued)
Subsets and Word Problems
We
can think of a subset as being “a selection” from a specified
group of objects. Think of the group of objects as a set. Then
the different ways the selection can be made are the subsets.
Example:
Jayne has four different color bracelets:
black (b), white (w), gold (g), and silver (s).
She is deciding which ones to wear today. What are her
choices? How many
choices does she have?
Solution:
Think of the bracelets she
has to choose from as a set
B = {b, w, g, s}.
Then her choices are all of the possible subsets of set
B.
Here is an organized way to list them:
|
0-element subsets |
1- element subsets |
2- element subsets |
3-element subsets |
4-element |
|
{
}
(She decides not to wear any
bracelet.) |
{b}
{w}
{g}
{s} |
{b, w}
{b, g}
{b, s}
{w, g}
{w, s}
{g, s} |
{b, w, g}
{b, w, s}
{w, g, s}
|
{b, w, g, s}
(She decides to wear all the
bracelets.) |
Jayne has 16 choices for which bracelets to wear today. Note
that 2 · 2 · 2 · 2 = 24 = 16. For each choice of color, Jayne can
either choose to wear the bracelet or not to wear the bracelet.
This idea of multiplying the
number of choices for each item to find the total number of
possibilities will be covered later in the course in Session 7
with the Fundamental Counting Principle.
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