FUNDAMENTAL COUNTING PRINCIPLE

PROBABILITY UNIT

What is the Fundamental Counting Principle?

The rule for finding the number of possible outcomes

States that if an event has “m” possible outcomes and another independent even has “n” possible outcomes, then there are mn (m times n) possible outcomes of the two events together.

Let Me Count The Ways. . .

Let's say that you want to flip a coin and roll a die.

There are 2 ways that you can flip a coin and 6 ways that you can roll a die.

There are then 2x6=12 ways that you can flip a coin and roll a die.

Let Me Count The Ways . . .

If you want to hit one note on a piano and play one string on a banjo

There are 88 notes on a piano and 5 strings on a banjo.

There are 88 * 5 = 440 ways to do both.

Let Me Count The Ways . . .

If you want to draw 2 cards from a standard deck of 52 cards without replacing them

There are 52 ways to draw the first and 51 ways to draw the second card (because we do not replace the first drawn card)

There are a total of 52*51 = 2652 ways to draw the two cards.

Now You Count The Ways . . . A phone number is a seven digit number

assigned by the phone company. How many different seven digit phone numbers can be assigned?

There are ten digits as possible outcomes for each placement in a phone number.

___ x ___ x ___ x ___ x ___ x ___x ___10

10

10

10

10

10

10

There are 10,000,000 possible outcomes for a seven digit phone number.

Now You Count The Ways . . . How many possible outfits can you make

from the clothing items listed below?SHIRTS

RED

WHITE

BLACK

PANTS

JEANS

KHAKIS

SHOES

TENNIS

BROWN

FLIP FLOPS

3 2 3 x x = 18

There are 18 outfit

combinations possible.

Now You Count The Ways . . . Say that you have 42

friends on Facebook. Any time you access your profile, 6 of your friends will appear in a box below your picture. Each time these friends are randomly generated out of your 42 friends. How many different arrangements of 6 people can show up?

____ x ____ x ____ x ____ x ____ x ____ = 42 41 40 39 38 37 3,776,965,920

Independent Practice:

Directions: On a piece of loose leaf paper, find the total possible outcomes for each situation. Show your work!

(1) You flip a coin five times. How many outcomes are possible?

(2) Dairy Queen offers two types of cones, twelve flavors of ice cream, and six different toppings. What is the greatest number of ice cream combinations you could order with one type of cone, one flavor, and one topping?

(3) Jocelyn has fifteen headbands and twenty-three bows. How many combinations of one headband and one bow can she make?