a2-7-08

a2-7-08 - Answers to Homework 7 February 2008 Section 15 1....

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Answers to Homework 7 February 2008 Section 15 1. Find all possible partitions of the set f 1 ; 2 ; 3 g . Classify them by how many sets are in the partition. One partition into one set ff 1 ; 2 ; 3 gg . Three partitions into two sets ff 1 g ; f 2 ; 3 gg , ff 2 g ; f 1 ; 3 gg , and ff 3 g ; f 1 ; 2 gg . One partition into three sets: ff 1 g ; f 2 g ; f 3 gg . Total of 1 + 3 + 1 = 5 partitions. Find all possible partitions of the set f 1 ; 2 ; 3 ; 4 g . One partition into one set: ff 1 ; 2 ; 3 ; 4 gg Four partitions with one one-element set: ff 1 g ; f 2 ; 3 ; 4 gg , ff 2 g ; f 1 ; 3 ; 4 gg , ff 3 g ; f 1 ; 2 ; 4 gg , ff 4 g ; f 1 ; 2 ; 3 gg Three partitions with two two-element sets: ff 1 ; 2 g ; f 3 ; 4 gg , ff 1 ; 3 g ; f 2 ; 4 gg , ff 1 ; 4 g ; f 2 ; 3 gg Six partitions into three sets: ff 1 ; 2 g ; f 3 g ; f 4 gg , ff 1 ; 3 g ; f 2 g ; f 4 gg , ff 1 ; 4 g ; f 2 g ; f 3 gg , ff 2 ; 3 g ; f 1 g ; f 4 gg , ff 2 ; 4 g ; f 1 g ; f 3 gg , ff 3 ; 4 g ; f 1 g ; f 2 gg One partition into four sets: ff 1 g ; f 2 g ; f 3 g ; f 4 gg Total of 1 + 4 + 3 + 6 + 1 = 15 partitions. 2. How many di/erent anagrams (including nonsensical words) can be made from each of the following : (a) STAPLE be any of 6 , the second letter any of the 5 remaining, and so on. The number of di/erent anagrams is 6! = 720 , which includes the original word STAPLE. (b) DISCRETE
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This note was uploaded on 07/13/2011 for the course MAD 2104 taught by Professor Staff during the Spring '08 term at FAU.

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a2-7-08 - Answers to Homework 7 February 2008 Section 15 1....

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