If set A has 5 elements and set B has 7 eleme | vedclass

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(D) Let $n(A) = 5$ and $n(B) = 7$. Total number of functions from $A$ to $B$ is given by $|B|^{|A|} = 7^5$. $A$ function is one-one if every element i

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$7^5-{ }^7 P_5$

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(D) Let $n(A) = 5$ and $n(B) = 7$. Total number of functions from $A$ to $B$ is given by $|B|^{|A|} = 7^5$. $A$ function is one-one if every element in $A$ maps to a distinct element in $B$. The number of one-one functions is given by $P(7, 5) = { }^7 P_5$. $A$ function is many-one if it is not one-one. Therefore,the number of many-one functions = (Total number of functions) - (Number of one-one functions) = $7^5 - { }^7 P_5$.

If set $A$ has $5$ elements and set $B$ has $7$ elements,then the number of many-one functions that can be defined from $A$ to $B$ is:

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