Problem 2. A Batch Made in Heaven (14 points) You are testing out new cookie recipes and decided to bring them into your Discrete Structures Seminar to share with your classmates. There are 34 students in your Seminar (everyone always comes to class), not including you. You do not need to account for yourself in any of the following problems. (a) [4 pts.] You have made 42 identical chocolate chip cookies. You are very generous and decide to give 3 to your instructor, leaving you with 39 cookies. In how many ways can you distribute the cookies to your 34 classmates? Note that it is possible a student gets 0 cookies. Describe how you arrived at your solution. (b) [5 pts.] You have also made 56 identical oatmeal raisin cookies. For these cookies, you want to make sure everyone of your classmates gets at least one. How many ways can you distribute the cookies given these constraints? Describe how you arrived at your solution. (c) I5 pts.] Finally, you have made 25 unique sugar cookies. That is, no two sugar cookies are the same. How many ways can you distribute the cookies to your classmates? Describe how you arrived at your solution. Note that it is necessary that some classmates won't get cookies, and that is okay. Solution