Suppose n > m. Let S be the collection of all functions from [n] to [m]. We randomly pick a function f from S. Define event A = {f is surjective}. (1). Find P[A] (2). What is the limit of P[A] as n →∞ and m is fixed?

Suppose n > m. Let S be the collection of all functions from [n] to [m]. We randomly pick a function f from S. Define event A = {f is surjective}. (1). Find P[A] (2). What is the limit of P[A] as n →∞ and m is fixed?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter3: The Derivative

Section3.CR: Chapter 3 Review

Problem 2CR

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Question

Suppose n > m. Let S be the collection of all functions from [n] to [m]. We randomly
pick a function f from S. Define event A = {f is surjective}.
(1). Find P[A]
(2). What is the limit of P[A] as n →∞ and m is fixed?

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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