Question

18. (5 points.) Note: For part (c), you will need to knou about the Catalan numbers. See the write-up on the "Content" page of DeL, or see Johnsonbaugh's tezt (in the 7th edition, pages 285-286, starting with Erample 6.2.22; in the 8th edtion, pages 275-276, starting with Erample 6.2.21). For your upcoming internship, you are in charge of bringing pastries to the daily meeting of the four executives of a company. (They are the President and the three Vice-Presidents in charge of Advertising, Pollution, and Price Gouging respectively.) (a) Suppose you arrive at the bakery one morning and see that they only have 6 donuts, 4 Danish, and 7 muffins left. These 17 pastries are all distinct. Suppose that you are required to buy exactly 5 donuts, 2 Danish, and 3 muffins. How many different ways could your bag be filled when you leave the bakery? (Order, such as "top of the bag to bottom of the bag," does not matter.) again, that they only have 6 donuts, 4 Danish, and 7 muffins left and that these 17 pastries are all distinct. Suppose that you are required to buy exactly four pastries, and the only requirement is that you buy at least one Danish. How many different ways could your bag be filled when you leave the bakery? them from the bag one at a time and lay them out on the conference table. Suppose also that, by decree of the Vice President in charge of Advertising, there may not be more muffins than Danish on the table at any time. Thus may remove the pastries in the order DDmmDaD, but not in the order DDDmmmmD. (You don't question the decree, you just follow it.) In how many ways can you remove the pastries from the bag? (c) Suppose you have already purchased 4 identical Danish and 4 identical muffins, and you are supposed to remove

Answer 1