Misc 4 (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 4 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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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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