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Find the Number of All onto Functions from the Set a = {1, 2, 3, ..., N} to Itself.

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Question

Find the number of all onto functions from the set A = {1, 2, 3, ..., n} to itself.

Sum
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Solution

We know that every onto function from A to itself is one-one.
So, the number of one-one functions = number of bijections = n!

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Chapter 2: Functions - Exercise 2.1 [Page 32]

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R.D. Sharma Mathematics Volume 1 and 2 [English] Class 12
Chapter 2 Functions
Exercise 2.1 | Q 16 | Page 32

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