Question

Let $A=\{a,b,c\}$ and $B=\{1,2,3,4\}$. Then the number of elements in the set $C=\{f:A\to B\mid 2\in f(A)$ and $f$ is not one-one $\}$ is_______.

Answer 1

Answer: 19.00

$C=\{f:A\to B\mid 2\in f(A)$ 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 $=19$