Question

For a function $f:A\to B,$ let the number of elements in set $A$ and $B$ be $4$ and $5$ respectively. If the number of many one functions are $N,$ then value of $\frac{N}{101}$ is

Answer 1

Here, we have $n\left(A\right)=4$ and $n\left(B\right)=5.$
Clearly $n\left(A\right)<n\left(B\right)$
So, the total number of functions $=5\times 5\times 5\times 5$
$=5^4=625$
The total number of one-one functions
$=5\times 4\times 3\times 2=120$
$\therefore$ Number of many one functions = total number of functions - number of one one functions
$=625-120=505$
So, $\frac{N}{101}=5$