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Let A be a set of n distinct elements. T...

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.

Text Solution

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The correct Answer is:
`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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