Question

For a function $f:A\to B$, the number of elements in set $A$ and $B$ are $5$ and $4$ respectively, then the number of many one functions are

Answer 1

Here, we have $n\left(A\right)=5$ and $n\left(B\right)=4.$
So, total number of functions $=4\times 4\times 4\times 4\times 4=4^5$
Number of one-one functions $=0(\because n(A)>n(B\left)\right)$
$\therefore$ Number of many one functions $=$ total functions $-$ one-one functions
$=1024-0=1024$