A mapping is select at random from the set of allthe mappings of the set `A={1,2, n}`into itself. Find the probability that the mappingselected is an injection.

A mapping is select at random from the set of allthe mappings of the s

1.	A mapping is select at random from the set of allthe mappings of the set `A={1,2, n}`into itself. Find the probability that the mappingselected is an injection.
Answer» The mapping is from set A to A. So, domain and codomain of function are A. Now, each pre-image in set A can be assigned any one of the images from set A. So, total number mappings = `n xx n xx n xx … xx n` (n times) = `n^(n)` Number of mappings which are one-one `= nxx (n-1) xx (n-2)xx ... xx 2 xx1 = n!` So, required probability = `(n!)/(n^(n)) = ((n-1)!)/(n^(n-1))`

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A mapping is select at random from the set of allthe mappings of the set `A={1,2, n}`into itself. Find the probability that the mappingselected is an injection.

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