Question

The number of onto functions (surjective functions) from set $X=\{1,2,3,4\}$ to set $Y=\{a,b,c\}$ is

• A. 36

Answer 1

The correct option is A 36

The number of onto functions from $A\to B$ where $|A|=m$ and $|B|=n$ is given by the formula
$n^m{-}^n{C}_1(n-1{)}^m{+}^n{C}_2(n-2{)}^m+\dots +(-1{)}^{n-1}{C}_{n-1}{1}^m$
Here, $m=4$ and $n=3$
Substituting in above formula we get,
$3^4{-}^3{C}_1(3-1{)}^4{+}^3{C}_2(3-2{)}^4$
$=81-48+3=36$