Question

If $A=\{1,2,3,4\}$ and $B=\{5,7,9\}$, then the number of onto function from $A$ to $B$ is

• A. $36$
• B. $45$
• C. $81$
• D. $64$

Answer 1

The correct option is A $36$

If the set $A$ has $n$ elements and set $B$ has $r$ elements, then the number of onto function from set $A$ to set $B$ is equivalent to distributing $n$ distinct objects into $r$ distinct boxes such that each box gets at least one object.

Total number of onto functions $=r^n-{}^r{C}_1(r-1{)}^n+{}^r{C}_2(r-2{)}^n-......$

Here, $n=4\&r=3$
$=3^4-{}^3{C}_1(3-1{)}^4+{}^3{C}_2(3-2{)}^4=81-48+3=36$