Let `A`be a set of `n`distinct elements. Then the total number of distinct function from `AtoA`is ______ and out of these, _____ are onto functions.

Let `A`be a set of `n`distinct elements. Then the total number of dist

1.	Let `A`be a set of `n`distinct elements. Then the total number of distinct function from `AtoA`is ______ and out of these, _____ are onto functions.
Answer» Correct Answer - `n^(n), overset(n)underset(r = 1)sum(-1)^(n - r) " "^(n)C_(r) (r)^(n)` Let `A = {x_(1), x_(2),..,x_(n)}` `therefore` Number of functions from A to A is `n^(n)` and out of these `overset(n) underset(r - 1)sum (-1)^(n-r)" "^(n)C_(r) (r)^(n)` are onto functions.

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Let `A`be a set of `n`distinct elements. Then the total number of distinct function from `AtoA`is __ and out of these, _ are onto functions.

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