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.

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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Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.

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