Question 1: A runner targets herself to improve her time on a certain course by 3 seconds a day. If on day 0 she runs the course in 3 minutes, how fast must she run it on day 14 to stay on target? A certain computer algorithm executes twice as many operations when it is run with an input of size k as when it is run with an input of size k − 1 (where k is an integer that is greater than 1). When the algorithm is run with an input of size 1, it executes seven operations. How many operations does it execute when it is run with an input of size 25? Question 2: Consider the letters in the word COMPUTER. a) In how many ways can these letters be arranged in a row? b) In how many ways can these letters be arranged if the letters CO must remain next to each other (in order) as a unit? Question 3: A multiple-choice test contains 10 questions. There are four possible answers for each question. a) In how many ways can a student answer the questions on the test if the student answers every question? b) In how many ways can a student answer the questions on the test if the student can leave answers blank? Question 4: How many ways are there to select 7 countries in the United Nations to serve on a council, if 2 are selected from a block of 45, 3 are selected from a block of 57, and the others are selected from the remaining 69 countries? A club has 25 members. a) How many ways are there to choose four members of the club to serve on an executive committee? b) How many ways are there to choose a president, vice president, secretary, and treasurer of the club, where no person can hold more than one office? Question 5: One hundred tickets, numbered 1, 2, 3, . . . , 100, are sold to 100 different people for a drawing. Four different prizes are awarded, including a grand prize. How many ways are there to award the prizes if: a) the person holding ticket 35 wins the grand prize? b) the person holding ticket 64 wins one of the prizes? c) the person holding ticket 18 does not win a prize? d) the people holding tickets 30 and 50 both win prizes?

Question 1: A runner targets herself to improve her time on a certain course by 3 seconds a day. If on day 0 she runs the course in 3 minutes, how fast must she run it on day 14 to stay on target? A certain computer algorithm executes twice as many operations when it is run with an input of size k as when it is run with an input of size k − 1 (where k is an integer that is greater than 1). When the algorithm is run with an input of size 1, it executes seven operations. How many operations does it execute when it is run with an input of size 25? Question 2: Consider the letters in the word COMPUTER. a) In how many ways can these letters be arranged in a row? b) In how many ways can these letters be arranged if the letters CO must remain next to each other (in order) as a unit? Question 3: A multiple-choice test contains 10 questions. There are four possible answers for each question. a) In how many ways can a student answer the questions on the test if the student answers every question? b) In how many ways can a student answer the questions on the test if the student can leave answers blank? Question 4: How many ways are there to select 7 countries in the United Nations to serve on a council, if 2 are selected from a block of 45, 3 are selected from a block of 57, and the others are selected from the remaining 69 countries? A club has 25 members. a) How many ways are there to choose four members of the club to serve on an executive committee? b) How many ways are there to choose a president, vice president, secretary, and treasurer of the club, where no person can hold more than one office? Question 5: One hundred tickets, numbered 1, 2, 3, . . . , 100, are sold to 100 different people for a drawing. Four different prizes are awarded, including a grand prize. How many ways are there to award the prizes if: a) the person holding ticket 35 wins the grand prize? b) the person holding ticket 64 wins one of the prizes? c) the person holding ticket 18 does not win a prize? d) the people holding tickets 30 and 50 both win prizes?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Discrete Structure

Question 1:

A runner targets herself to improve her time on a certain course by 3 seconds a day. If on day 0 she runs the course in 3 minutes, how fast must she run it on day 14 to stay on target?

A certain computer algorithm executes twice as many operations when it is run with an input of size k as when it is run with an input of size k − 1 (where k is an integer that is greater than 1). When the algorithm is run with an input of size 1, it executes seven operations. How many operations does it execute when it is run with an input of size 25?

Question 2:

Consider the letters in the word COMPUTER.

a) In how many ways can these letters be arranged in a row?
b) In how many ways can these letters be arranged if the letters CO must remain next to each other (in order) as a unit?

Question 3:

A multiple-choice test contains 10 questions. There are four possible answers for each question.

a) In how many ways can a student answer the questions on the test if the student answers every question?
b) In how many ways can a student answer the questions on the test if the student can leave answers blank?

Question 4:

How many ways are there to select 7 countries in the United Nations to serve on a council, if 2 are selected from a block of 45, 3 are selected from a block of 57, and the others are selected from the remaining 69 countries?

A club has 25 members.
a) How many ways are there to choose four members of the club to serve on an executive committee?
b) How many ways are there to choose a president, vice president, secretary, and treasurer of the club, where no person can hold more than one office?

Question 5:

One hundred tickets, numbered 1, 2, 3, . . . , 100, are sold to 100 different people for a drawing. Four different prizes are awarded, including a grand prize. How many ways are there to award the prizes if:

a) the person holding ticket 35 wins the grand prize?
b) the person holding ticket 64 wins one of the prizes?
c) the person holding ticket 18 does not win a prize?
d) the people holding tickets 30 and 50 both win prizes?

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