(a) How many one-to-one functions are there from a set with four elements to a set with five elements? There are 120 choices for where to send the first element of the domain, 5 (b) How many one-to-one functions are there from a set with four elements to a set with three elements? 0 choices for where to send the second element of the domain, and so forth. Thus, the total number of one-to-one functions is 120 (c) How many one-to-one functions are there from a set with four elements to a set with four elements? 24 (d) How many one-to-one functions are there from a set with four elements to a set with six elements? 360 (e) How many one-to-one functions are there from a set with m elements to a set with n elements, where m s n? n!
(a) How many one-to-one functions are there from a set with four elements to a set with five elements? There are 120 choices for where to send the first element of the domain, 5 (b) How many one-to-one functions are there from a set with four elements to a set with three elements? 0 choices for where to send the second element of the domain, and so forth. Thus, the total number of one-to-one functions is 120 (c) How many one-to-one functions are there from a set with four elements to a set with four elements? 24 (d) How many one-to-one functions are there from a set with four elements to a set with six elements? 360 (e) How many one-to-one functions are there from a set with m elements to a set with n elements, where m s n? n!
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.6: Inequalities
Problem 80E
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