Chapter 10 Section 1 Apply the Counting Principle and Permutations In this assignment, you will be able to Use the Fundamental Counting Principle. 1. Use a tree diagram. 3. Use the Counting Principle with Repetition. 4. Find the Number of Permutations

1.) 2.) A sporting goods store offers 3 types of snowboards (all- mountain, freestyle, and carving) and 2 types of boots (soft and hybrid). Draw a tree diagram to determine how many choices the store offers for snowboarding equipment? You are framing a picture. The frames are available in 12 different styles. Each style is available in 55 different colors. You also want blue mat board, which is available in 11 different shades of blue. How many different ways can you frame the picture?

1.) 2.) All Mountain < Freestyle < Carving < Soft Hybrid Soft Hybrid Soft Different ways Answers:

3.) The standard configuration for a Texas license plate 1 letter followed by 2 digits followed by 3 letters. a.) How many different license plates are possible if letters and digits can be repeated? b.) How many different license plates are possible if letters and digits cannot be repeated?

3.) a.) b.) Answers:

4.) Ten teams are competing in the final round of the Olympic four person bobsledding competition. a.) In how many different ways can the bobsledding teams finish the competition. (Assuming there are no ties). b.)In how many different ways can 3 of the bobsledding teams finish first, second and third to win the gold, silver and bronze medals?

4.) Answers: a.) b.)

5.) An object has an attribute from each list. Make a tree diagram that shows the number of different objects that can be created. T-Shirts Size: M, L, XL Type: long-sleeved, short sleeved 6.)Meal Entree: chicken, fish, pasta Side: corn, green beans, potato

5.) Answer: short sleeved 6.) Chicken Fish Corn Long sleeved M XL L M L Pasta 6 ways Green beans Potato Green beans Corn 9 ways

You want some toast. The restaurant offers white, French, rye or wheat bread. For a topping, you can have strawberry jam, grape jelly, peanut butter or butter. How many ways can you have toast? 7.) 8.) You want to purchase a class ring. The ring can be made from three different metals Auralite, Gold or Silver. You can choose from six different side designs, Academics, Art, Athletics, Literature, Music or Technology and 12 different stones. How many rings are possible.

7.) 8.) Answer: 216 class rings 16 different kinds of toast

9.) 10.) 11.) 12.) For the given configuration, determine how many different license plates are possible if (a) digits and letters can be repeated, and (b) digits and letters cannot be repeated. 4 letters followed by 3 digits 1 letters followed by 5 digits 5 digits followed by 3 letters 6 letters

9.) 10.) 11.) 12.) Answer: a.) 456,976,000 license plates b.) 258,336,000 license plates a.) 2,600,000 license plates a.) 1,757,600,000 license plates b.) 786,240 license plates b.) 471,744,000 license plates b.) 165,765,600 license plates a.) 308,915,776 license plates

A photographer lines up 15 members of a family in single line in order to take a photograph. How many different ways can the photographer arrange the family members for the picture? 13.)

Answer: 1,307,674,368,000 ways

14.) A Spanish club is electing a president, vice- president, and secretary. The club has 9 members who are eligible for these offices. How many different ways can these 3 offices can be held?

Answer: 14.)504 ways

15.) Let's look at your locker combination. There are 40 numbers, and you need to enter 3 numbers. How many combinations are there? a.) b.) What if the lock changed from numbers to letters and they added a forth combo. How many combinations are there? c.)Which lock is better and why?

15.) a.) b.) c.) Answer: 64,000 combinations 456,976 combinations B has more combinations, there fore harder to break in to.