If a set A has n elements,then the number of | vedclass

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(C) The total number of functions from a set $A$ with $n$ elements to itself is $n^n$.$A$ function is one-one if every element in the domain has a uni

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$n^{n} - n!$

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(C) The total number of functions from a set $A$ with $n$ elements to itself is $n^n$.$A$ function is one-one if every element in the domain has a unique image in the codomain. For a set with $n$ elements,the number of one-one functions is given by the number of permutations of $n$ elements,which is $n!$.Therefore,the number of functions that are not one-one is the total number of functions minus the number of one-one functions.Number of functions that are not one-one $= n^n - n!$.

If a set $A$ has $n$ elements,then the number of functions defined from $A$ to $A$ that are not one-one is

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