CS 30 : Discrete Mathematics for Computer Science First Semester, AY 2012-2013

https://sites.google.com/a/dcs.upd.edu.ph/nhsh_classes/cs30

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Nestine Hope S. Hernandez Algorithms and Complexity Laboratory Department of Computer Science University of the Philippines, Diliman nshernandez@dcs.upd.edu.ph

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Day 12 dcs-logo

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Discrete Mathematics for Computer Science

CS 30

HOMEWORK I

1

How many 8-letter words with 3 dierent vowels and 5 dierent consonants can be formed from the English alphabet?

2

How many ways can 20 similar books be placed on 5 dierent

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shelves? 3

How many ways can the letters of the English alphabet be arranged so that there are exactly 5 letters between the letter A and the letter B?

4

Eleven players have gathered to play 5 on 5 basketball. (a) If they have decided that one of the teams will have 6 players and use a substitute, then how many ways are there for them to break up into two teams?

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(b) If one player decide to leave and there are only 10 players left, then how many ways are there to break up into two teams of 5?

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Discrete Mathematics for Computer Science

CS 30

HOMEWORK II

5

How many ways are there to seat 5 girls at a circular table where the particular seat taken by each girl does not matter but what matters to each girl is (a) who is sitting to her left and who is sitting to her right

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(b) who is sitting next to her (doesn't matter w/c side) 6

Find the number of ways to partition 10 students into 4 teams so that 2 teams contain 3 students and 2 teams contain 2 students

7

How many ways can you solve

k1 , k2 , k3 8

and

k4

k1 + k2 + k3 + k4 = 18 provided k1 , k2 ≥ 0, k3 ≥ 3, k4 ≥ 2?

that

are integers and

How many positive integers not exceeding 1000 are not divisible by 3, 5, or 7?

9

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How many permutations of the 26 letters of the English alphabet does not contain the strings ten, algorithm or compute?

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Discrete Mathematics for Computer Science

CS 30

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Questions? See you next meeting!

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Discrete Mathematics for Computer Science

CS 30