CSE-21.ProblemSet_1

CSE-21.ProblemSet_1 - letter can be used more often than it...

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Jonathan Thomas Guidry CSE-21 1. (1 pt) In a certain land on a planet in a galaxy far away the alphabet contains only 5 letters which we will transliterate as A, B, C, D, and E. All names are 6 letters long, begin and end with consonants and contain exactly two vowels, which cannot be adjacent to each other. Also, adjacent consonants must be different from each other. How many possible names are there? 2. (3 pts) We want to know how many ways 4 boys and 3 girls can sit in a row. (a) How many ways can this be done if there are no restrictions? (b) How many ways can this be done if the boys sit together and the girls sit together? (c) How many ways can this be done if no boy sits next to an- other boy? 3. (3 pts) We are interested in forming 3 letter words using the letters in SASSAFRAS. For the purposes of the problem, a “ word ” is any list of letters. (a) How many words can be made with no repeated letters? (b) How many words can be made with unlimited repetition al- lowed? (c) How many words can be made if repeats are allowed but no
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Unformatted text preview: letter can be used more often than it appears in SASSAFRAS? 4. (3 pts) The Dean at a certain college wants to form 3-person committees from members of the 4 departments that re-port to him. These departments and their sizes are: CSE - 40, ECE - 35, Math - 30, Physics - 25. How many possible commit-tees are there if: (a) committees have no two members from the same depart-ment; (b) committees cannot have all three members from the same department; (c) committees have no two members from the same depart-ment, and further do not have members from both CSE and ECE. 5. (1 pt) A certain computer system requires passwords con-sisting of exactly 6 characters from the 5 letters { A , B , C , D , E } and the 5 digits { , 1 , 2 , 3 , 4 } which have at least one letter and and least one digit. How many possible passwords like this are there? Generated by the WeBWorK system c WeBWorK Team, Department of Mathematics, University of Rochester 1...
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