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程序代写案例-MA1510-Assignment 2
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University of Aberdeen Department of Mathematics Author Irakli Patchkoria Date 10.03.2023 Code MA1510 Combinatorics Assignment 2 >Deadline for submission is 23:00 Friday March 17th, 2023. Submit it on Myaberdeen, 20 points in total. Justify your answers and SHOW ALL WORKING. Poor presentation may result in the loss of marks. How many ways are there to distribute 17 sweets among 12 children so that each child1. gets at least 1 sweet. Leave the answer in terms of binomial coefficients (sweets are indistinguishable as always) [5 marks]. Let S = {1, 2, 3, 4, 5, 6, 7}.2. 1. Is the set A = {{1, 2}, {3, 4}, {1, 4}, {5}, {6, 7}} a partition of S? Justify your answer [1 mark]. 2. Is the set A = {{1, 2}, {3, 4}, {6, 7}} a partition of S? Justify your answer [1 mark]. 3. Write down a partition A of S such that exactly two parts of A consist of 3 elements (i.e., exactly two parts of A consist of 3 elements) [3 marks]. 3. 1. Compute the inverse of the formal power series f(t) = 1 + t 2 + t2 4 + t3 8 + · · ·+ t n 2n + · · · = ∞∑ n=0 tn 2n . [3 marks] 2. Let n ≥ 4. Show that the Fibonacci numbers satisfy the relation Fn = 2Fn−3 + Fn−2 + Fn−4. [2 marks] Suppose we have 5 boxes with different colours: green, yellow, white, blue, and red4. boxes. Also suppose that we have 5 books with different colours: green, yellow, white, blue, and red books. We want to put all these books in the boxes, so that no two books end up in the same box, and no book ends up in a box with the same colour. How many ways are there to do this? (Justify your answer. Just writing down the number will not be enough) [5 marks].
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