This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math 15B Midterm Exam Solutions 26 October 2001 1. Give an example of each of the following or explain why it cannot be done. (a) A bijection from { 1 , 2 , 3 , 4 } to { a, b, c } . A. Impossible. A bijection has its range and domain the same size. (b) A permutation of { 1 , 2 , 3 , 4 , 5 , 6 , 7 } that has a cycle of length 4 and also has a cycle of length 5. A. Impossible. The sum of cycle lengths is the size of the set being permuted and 4 + 5 > 7. 2. A committee contains 7 women and 6 men. We want to form a subcommittee with 5 of these people. (a) How many ways can this be done? A. ( 7+6 5 ) (b) How many ways can this be done if the subcommittee must contain at least 2 women and at least 2 men? A. There are either (2 men AND 3 women) OR (3 men AND 2 women). By the Rules of Sum and Product, the answer is ( 6 2 ) ( 7 3 ) + ( 6 3 ) ( 7 2 ) . Choosing two of each sex and then a fifth committee member via ( 6 2 )( 7 2 )( 9 1 ) over counts. For example, if there are 3 women on the committee, the committee iscounts....
View Full Document
 Fall '01
 Bender
 Math

Click to edit the document details