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The Principle of Inclusion-Exclusion can be used to solve the following problems. 1. How many functions f: {1,2,..., 7} → {1,2,3,4} are surjective?

The Principle of Inclusion-Exclusion can be used to solve the following problems. 1. How many functions f: {1,2,..., 7} → {1,2,3,4} are surjective?

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.1: Postulates For The Integers (optional)
Problem 29E
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The Principle of Inclusion-Exclusion can be used to solve the following problems. 1. How many functions f : {1,2,..., 7} - → {1,2,3,4} are surjective? 2. Count the number of integers in the range 1 to 10¹0 are not perfect squares, cubes, or fifth powers. That is, the integer cannot be written in the form m" where m is an integer and ris one of 2,3,5. 3. Count the number of arrangements of the 10 letters ABCDEFGHIJ in which none of the patterns ABE, BED, or HID occur.
Transcribed Image Text:The Principle of Inclusion-Exclusion can be used to solve the following problems. 1. How many functions f : {1,2,..., 7} - → {1,2,3,4} are surjective? 2. Count the number of integers in the range 1 to 10¹0 are not perfect squares, cubes, or fifth powers. That is, the integer cannot be written in the form m" where m is an integer and ris one of 2,3,5. 3. Count the number of arrangements of the 10 letters ABCDEFGHIJ in which none of the patterns ABE, BED, or HID occur.
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