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Q.
Let $A=\{a, b, c\}$ and $B=\{1,2,3,4\}$. Then the number of elements in the set $C=\{f: A \rightarrow B \mid 2 \in f(A)$ and $f$ is not one-one $\}$ is_______.
JEE MainJEE Main 2020Relations and Functions - Part 2
Solution:
$C=\{f: A \rightarrow B \mid 2 \in f(A)$ and $f$ is not one-one $\}$ Case-I : If $f ( x )=2 \forall x \in$ A then number of function $=1$ Case-II : If $f(x)=2$ for exactly two elements then total number of many-one function $={ }^{3} C _{2}{ }^{3} C _{1}=9$ Case-III : If $f ( x )=2$ for exactly one element then total number of many-one
functions $={ }^{3} C _{1}{ }^{3} C _{1}=9$
Total $=19$