Question

Let $E=\{1,2,3,4\}$ and $F=\{1,2\},$ then the number of onto functions from $E$ to $F$ is

Answer 1

$E=\{1,2,3,4\}$ and $F=\{1,2\},$
If $n\left(E\right)=m$ and $n\left(F\right)=n,$ where $1\le n\le m,$ then number of onto functions from $A$ to $B$
$=n^m-{(}^n{C}_1(n-1{)}^m{-}^n{C}_2(n-2{)}^m+\dots )$
$(\because m=4,n=2,m>n)$
$=2^4-{(}^2{C}_1(2-1{)}^4)$
$=16-2=14$