Let $A=\{a,b,c\}andB=\{1,2,3,4\}.$ Then the number of elements in the set  $C=\left\{f:A\to B/3\in f\left(A\right)andf\text{\hspace{0.17em}is\hspace{0.17em}not}\text{\hspace{0.17em}one-one}\right\}$ is _______________ 

The desired functions will contain either one element or two elements in its codomain of which’3’ always belongs to  $f\left(A\right)$

$\therefore ThesetBcan\left\{3\right\},\{1,3\},\{2,3\},\{3,4\}$

Total number of functions = $1+(2^3-2)3=19.$