(iii) The photographer realizes that 60 (sixty) people in a row is way too wide
ID: 3184465 • Letter: #
Question
(iii) The photographer realizes that 60 (sixty) people in a row is way too wide for a clean picture, so they ask the people to instead split into 3 (three) rows of 20 (twenty) people each. How many photos of all the students carn they take now? Note that it is assumed that the photographer has already chosen the splitting of the people across rows. We further assume that every student stays in their row, that is, no student will move from one row to another (7 pts) (f) Renowned French chef Pierre Blaireau is planning a five-course meal for his restaurant's guests. His different choices include 10 (ten) light appetizers, 12 (twelve) salads, 5 (five)small risotto-based entrées, 7 (seven) seafood-based dishes and 5 (five) desserts (i) Chef Blaireau inspects his ingredients for quality and freshness and throws away 3 (three) salads and 2 (two) kinds of seafood. How many five-course meals can he make after this? (2 pts) (ii) After chef Blaireau has thrown away the aforementioned ingredients, a couple arrives at the restaurant to enjoy the five-course meal. They decide to take 2 (two) of each category of food (appetizer, meat entreée, etc.). In addition, they do not want to pick the same kind of food for any course, since they want to share it anyway. Finally, since they want to share their food, it does not matter who the waiter gives the dishes to That is, order between the two customers does not matter; as far as they are concerned, both dishes could be placed in the middle, between them. How many different five-course meals can be served in the couple's table? (5 pts)Explanation / Answer
(iii)no. Of ways = (20!)^3
f (I) no. Of five course meals=10*(12-3)*5*(7-2)*5=11250
(iI)no. Of five course meals for couple=10C2*9C2*5C2*5C2*5C2=1620000
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