Misc 10 - Find number of all onto functions from {1, 2, 3 .. n} - Miscellaneous

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  1. Chapter 1 Class 12 Relation and Functions
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Misc 10 (Introduction) Find the number of all onto functions from the set {1, 2, 3, … , n} to itself. Taking set {1, 2, 3} Since f is onto, all elements of {1, 2, 3} have unique pre-image. Total number of one-one function = 3 × 2 × 1 = 6 Misc 10 Find the number of all onto functions from the set {1, 2, 3, … , n} to itself. Since f is onto, all elements of {1, 2, 3} have unique pre-image. Total number of onto functions = n × n –1 × n – 2 × …. × 2 × 1 = n!

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