PERMUTATIONS AND COMBINATIONS 1. Explain the difference between permutations and combinations. 2. There are 13 flavors at the soda machine, and anyone can choose 6. A sign says we are only allowed to use one of each flavor. You decide to grab a cup and fill it up with your favorite flavors at random (it's all going to the same place, right?). How many possible soda mixtures can you make? Make sure to show your work and provide a numerical answer (i.e., don't leave it in factorial form). 3. Part 1: The manager of the soda shop decides that because you are a good customer, you may use a flavor as many times as you'd like. How many different possible mixtures can you make now (remember, you have 13 flavors available to you and you must choose 6)? Show your work and leave your answer in exponential or factorial form. Part 2: You realize that, despite what you expected, the soda actually tastes different depending on which flavor you choose first, second, etc. With this in mind, how many different sodas can you make if repetition is not allowed? Show your work and leave your answer in exponential or factorial form