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 1 st row is first coin 2 nd row is the second coin 3 rd row is the third coin. You are listing out the possibilities.

HHH, HHT, HTH, HTT, TTH, TTT, THH, THT  Begin H H T H T TH T HT H H T T

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), … ◦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