**
Readings for Session 9 – (Continued)
**

**Fundamental Counting Principle**

**
Fundamental Counting
Principle**

The Cartesian product form for
multiplication is the basis for the Fundamental Counting
Principle. This
principle tells us that if there are “*a*”
ways to do task *A* and “*b*” ways to do
another task *B*, there
are *a*
×
*b*
ways to do task *A* followed by task *
B*.

*Example:* You have
three t-shirts and two pairs of shorts.
In how many ways can you choose one t-shirt and one pair
of shorts to wear?

*Answer:* We have two
distinct sets of objects, t-shirts (*T*)
and shorts (*S*).

*n*(*T*)
∙
*n*(*S*)
= *n*(*T*
×
*S*) = 6

You have six choices for an outfit of one t-shirt and one pair of shorts.

Notice that the tree diagram for the above problem was
easily drawn out as a tree diagram to illustrate all the ordered
pairs of t-shirts and shorts. But, for problems with a large
number of objects, the Fundamental Counting Principle gives a
short-cut way of counting the number of end-branches in a tree
diagram without needing to draw out the entire diagram.

*Example:* A coin
is tossed, a die is rolled, and a card is drawn from a standard
deck. How many outcomes are possible?

Notice that a tree diagram for this problem would take a lot of
time to draw out with all the possibilities. So, we apply the
Fundamental Counting Principle to count all the ordered triplets
for the coin, die, and card such as

(H, 3, ace of hearts) or (T, 2, queen of clubs).

*n*(coin)
∙
*n*(die)
∙
*n*(card) = 2
∙
6
∙
52 = 624

There would 624 possible outcomes when a coin is tossed, a die
is rolled, and a card is drawn.

*
*

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