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

sablay-logo

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

updilseal

Day 12 dcs-logo

acl-logo

Discrete Mathematics for Computer Science

CS 30

HOMEWORK I

1

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

2

How many ways can 20 similar books be placed on 5 dierent

sablay-logo

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?

updilseal

(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?

dcs-logo

acl-logo

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

sablay-logo

(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

updilseal

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

dcs-logo

acl-logo

Discrete Mathematics for Computer Science

CS 30

sablay-logo

Questions? See you next meeting!

updilseal

dcs-logo

acl-logo

Discrete Mathematics for Computer Science

CS 30

[Hernandez 1213A] Cs30 day12