Answer each of the following questions. You do not need to give the final numeric value. 1. (2.5 pt.) A basket holds a set of balls. Each ball is either red, green, or blue. How many balls must there be in the basket to guarantee that there are at least 5 of the same color? 2. (2.5 pt.) A password must be 6 characters long and contain only digits and lowercase English letters. The English alphabet contains 21 consonants and 5 vowels. How many different passwords contain at least one vowel? 3. (2.5 pt.) How many different bit strings of length 8 start with 0 or contain the same number of 0's and 1's? 4. (2.5 pt.) A standard deck of playing cards consists of 52 cards. Each card has a rank and a suit. There are 13 possible ranks (A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K), 4 possible suits (spades, clubs, diamonds, hearts), and 13 cards for each suit. How many different hands of 5 cards contain 3 cards of one suit and 2 cards of a different suit (for example, 3 hearts and 2 diamonds)? 5. (2.5 pt.) 10 cookies are given to 10 kids. There are 5 chocolate chip cookies, 3 sugar cookies, and 2 oatmeal cookies. Assuming that each kid gets one cookie, how many different ways are there to give the cookies to the kids? 6. (2.5 pt.) A bakery sells 20 varieties of cupcakes. How many different ways are there to choose a dozen cupcakes if at most 6 are blueberry cupcakes?
Answer each of the following questions. You do not need to give the final numeric value. 1. (2.5 pt.) A basket holds a set of balls. Each ball is either red, green, or blue. How many balls must there be in the basket to guarantee that there are at least 5 of the same color? 2. (2.5 pt.) A password must be 6 characters long and contain only digits and lowercase English letters. The English alphabet contains 21 consonants and 5 vowels. How many different passwords contain at least one vowel? 3. (2.5 pt.) How many different bit strings of length 8 start with 0 or contain the same number of 0's and 1's? 4. (2.5 pt.) A standard deck of playing cards consists of 52 cards. Each card has a rank and a suit. There are 13 possible ranks (A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K), 4 possible suits (spades, clubs, diamonds, hearts), and 13 cards for each suit. How many different hands of 5 cards contain 3 cards of one suit and 2 cards of a different suit (for example, 3 hearts and 2 diamonds)? 5. (2.5 pt.) 10 cookies are given to 10 kids. There are 5 chocolate chip cookies, 3 sugar cookies, and 2 oatmeal cookies. Assuming that each kid gets one cookie, how many different ways are there to give the cookies to the kids? 6. (2.5 pt.) A bakery sells 20 varieties of cupcakes. How many different ways are there to choose a dozen cupcakes if at most 6 are blueberry cupcakes?
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Transcribed Image Text:Answer each of the following questions. You do not need to give the final
numeric value.
1. (2.5 pt.) A basket holds a set of balls. Each ball is either red, green, or blue. How
many balls must there be in the basket to guarantee that there are at least 5
of the same color?
2. (2.5 pt.) A password must be 6 characters long and contain only digits and
lowercase English letters. The English alphabet contains 21 consonants and 5
vowels. How many different passwords contain at least one vowel?
3. (2.5 pt.) How many different bit strings of length 8 start with 0 or contain the
same number of 0's and 1's?
4. (2.5 pt.) A standard deck of playing cards consists of 52 cards. Each card has a
rank and a suit. There are 13 possible ranks (A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K),
4 possible suits (spades, clubs, diamonds, hearts), and 13 cards for each suit.
How many different hands of 5 cards contain 3 cards of one suit and 2 cards
of a different suit (for example, 3 hearts and 2 diamonds)?
5. (2.5 pt.) 10 cookies are given to 10 kids. There are 5 chocolate chip cookies, 3
sugar cookies, and 2 oatmeal cookies. Assuming that each kid gets one cookie,
how many different ways are there to give the cookies to the kids?
6. (2.5 pt.) A bakery sells 20 varieties of cupcakes. How many different ways are
there to choose a dozen cupcakes if at most 6 are blueberry cupcakes?
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