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8 5 points note for part c you will need...

Question: 8 5 points note for part c you will need...

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8. (5 points.) Note: For part (c), you will need to kmow about the Catalan numbers. See the write-up on the Content page of DeL, or see Johnsonbaughs tezt (in the 7uh edition, pages 285-286, starting with Erample 6.2.22; in the šth 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 exeeutsa 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 let These 17 pastries are all distinct. Suppose that you are required to buy exactly 5 donuts, 2 Danish, ands How many different ways could your bag be filled when you leave the bakery? (Order, such as top bottom of the bag, does not matter.) are all distinct. (b) Suppose, again, that they only have 6 donuts, 4 Danish, and 7 mufins left and that these 17 pastries Suppose that you are required to buy exactly four pastries, and the only requirement i Danish. How many different ways could your bag be filled when you leave the bakery is that you buy at least one (c) Suppose you have already purchased 4 identical Danish and 4 identical muffins, and you are supposed e them from the bag one at a time and lay them out on the conference table. Suppose also President in charge of Advertising, there may not be more muffins than Danish on the t that, by decree of the able at any time. T Vice you hus may remove the pastries in the order DDmmDmDa, but not in the order DDDD(You dont question t just follow it.) In how many ways can you remove the pastries from the bag?

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