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Unformatted text preview: Fall 2009 CS131 – Combinatorial Structures Homework 1 Homework 1, due Sept 15 You must prove your answer to every question. Do not rely only on the homework for exercise: there are several self-check ex- ercises of the easier kind in the book, try to solve them, too! Problem 1 (LPV 1.8.28) . You want to send postcards to 12 friends. In the shop there are only 3 kinds of postcard. In how many ways can you send the postcards, in each of the following cases? (a) (5pt) There is large number of each kind of postcard, and you want to send one card to each friend. Solution. I can send 3 possible postcards to the first friend; for each of these choices, I have 3 possibilities for the second friend, and so on. So the total number is 3 · 3 ··· 3 = 3 12 . (b) (5pt) There is a large number of each kind of postcard, and you are willing to send one or more postcards to each friend (but no one should get two identical cards). Solution. Again, there are no dependences between my choices for each friend. To each friend, I can send each of the 7 nonempty subsets of the 3 kinds of postcard, so the total number of possibilities is 7 12 ....
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