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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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प्रश्न

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

योग
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उत्तर

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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अध्याय 2: Functions - Exercise 2.1 [पृष्ठ ३२]

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आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
अध्याय 2 Functions
Exercise 2.1 | Q 16 | पृष्ठ ३२

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