rec0510_ans - COT3100 Summer2001 Recitation 05/10...

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COT3100 Summer’2001 Recitation 05/10 Combinatorics. 1. Consider a set of five distinct computer science books, three distinct math books, and two distinct art books. a) In how many ways can these books be arranged on a shelf? 10! b) In how many ways can these books be arranged on a shelf if all five computer science books are on the left and both art books are on the right? 5! 3! 2! In how many ways can these books be arranged on a shelf if all books of the same discipline are grouped together? 5! 3! 2! 3! c) In how many ways can these books be arranged on a shelf if the two art books are not together? There are 9! arrangements where two art books are together. Then there are (10!-2 9!) arrangements where two art books are not together. ( 9! arrangements for each of two permutations of two art books). Ans: 8 9! 2. a) How many integers should be selected from the first 10 positive integers (1, 2, …10) to ensure that there exists a pair of these integers with the sum equal 11? 6
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rec0510_ans - COT3100 Summer2001 Recitation 05/10...

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