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Answer the following questions. Give justifications and explanations when needed. c) At an organization in the US, all phone numbers are 7 digits long and start with either 716 or 718. How many different phone numbers are there in which the last four digits are all different? d) Bob has 5 homework assignments but has time to do only 3 of them. In how many ways can Bob choose 3 homework assignments? e) Show that if 6 integers are chosen at random, at least two numbers will have the same remainder when divided by 5. Use pigeonhole principle.

Answer the following questions. Give justifications and explanations when needed. c) At an organization in the US, all phone numbers are 7 digits long and start with either 716 or 718. How many different phone numbers are there in which the last four digits are all different? d) Bob has 5 homework assignments but has time to do only 3 of them. In how many ways can Bob choose 3 homework assignments? e) Show that if 6 integers are chosen at random, at least two numbers will have the same remainder when divided by 5. Use pigeonhole principle.

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.7: Problem Solving: Consecutive Integers
Problem 12OE
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Answer the following questions. Give justifications and explanations when needed. c) At an organization in the US, all phone numbers are 7 digits long and start with either 716 or 718. How many different phone numbers are there in which the last four digits are all different? d) Bob has 5 homework assignments but has time to do only 3 of them. In how many ways can Bob choose 3 homework assignments? e) Show that if 6 integers are chosen at random, at least two numbers will have the same remainder when divided by 5. Use pigeonhole principle.
Transcribed Image Text:Answer the following questions. Give justifications and explanations when needed. c) At an organization in the US, all phone numbers are 7 digits long and start with either 716 or 718. How many different phone numbers are there in which the last four digits are all different? d) Bob has 5 homework assignments but has time to do only 3 of them. In how many ways can Bob choose 3 homework assignments? e) Show that if 6 integers are chosen at random, at least two numbers will have the same remainder when divided by 5. Use pigeonhole principle.
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