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 $\dots$

only $\text{'}2\text{'}$ in range $\to 1$ function.

Total no of many one function without any condition = 60-24=40.

Number of many one function with 2 is not in range =27-6 =21.

Therefore no of not one-one functions with 2 in range = 40-21=19.