Counting Principles Assignment 1. Tree Diagrams a. Construct a tree diagram and determine the number of different sundaes that can be ordered if there are 2 types of ice cream (chocolate and vanilla) and 3 sauces (chocolate, caramel, and strawberry). b. Extend your tree diagram to include the option of requesting sprinkles, and determine the new number of sundaes. 2. Your family is considering purchasing a new car. The dealer has given a list of choices that need to be made. The interior may be made of cloth or leather and comes in tan, gray, or black. The vehicle is available as standard or automatic. Your family must also decide if air conditioning is needed. a. Illustrate the situation using a tree diagram. b. Determine the number of different vehicles available. c. Use the fundamental counting principles to conrm your answer to b). 3. A student needs to select a writing utensil from their pencil case to take down a very important note on the three measures of central tendency. They have 5 different pens and 3 different pencils. a. How many different writing utensils might that student use to take the note? b. This particular student is extremely meticulous. They use a pen for definitions and pencil for examples. How many different combinations of writing utensils might they use now? 4. A golfer has 8 shirts, 6 pairs of shoes, 15 pairs of socks, and 4 pairs of pants. How many different outts can he wear