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Counting

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Counting

Chapter 13 sec 1

- Break up into groups

- One method of counting is using the tree diagram.
- It is useful to keep track of counting.
- Order of permutations does matter.

- You will determine all the possible ways to count.
- Remember order matters!!

- How many ways can we do each of the following?
- Flip a coin?
- 2 ways; One head and one tails.

- Roll a single die?
- 6 ways
- Pick a card from a standard deck of cards?
- 52 ways

- Example; How many ways can 3 coins be flipped?
- How would you list the ways?
- How would you list the possibilities?

- Make a tree diagram
- 1st row is first coin
- 2nd row is the second coin
- 3rd row is the third coin.
- You are listing out the possibilities.

- Begin

H

T

T

H

T

H

H

T

H

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- How about rolling two dice?
- Let us say that one die is red and the other is green.

- In your group see if you can find all combinations.
- Starting with
- (1,1), (1,2), (1,3), …
- 36 ways.

- If objects are allowed to be used more than once in a counting problem, we will use the phrase with repetition.
- If we do not want objects to be used more than once, without repetition.

- Draw a tree diagram that illustrates the different ways to flip a dime, penny, quarter, and nickel.
- 1. In how many ways can you get exactly one head?
- 4

- 2. In how many ways can you get exactly two tails?
- 6

- 3. How many different three-digit numbers can you form using the digits 1, 2, 5, 7, 8, & 9 without repetition?

- 120

- You are a designer and has designed different tops, pants, and jackets to create outfits for a runway show. Without repetition, how many different outfits can your models wear if you had designed the following:
- Seven tops, six pants, three jackets.

- 126