The number of one one functions that can be defined from $A=\left\{1,2,3,4,5\right\}$ into $B=\left\{a,b,c,d\right\}$ is

The number of one one function from the set A to the set B is $n{\left(B\right)}_{P_{n\left(A\right)}} if n\left(B\right) \ge n\left(A\right)$

$and 0 if n\left(B\right)<n\left(A\right)$

Given $A=\left\{1,2,3,4,5\right\}$ and $B=\left\{a,b,c,d\right\}$

Here $n\left(A\right)=5,n\left(B\right)=4$

Here the number of elements in the codomain set is less than the number of elements of the domain set

Therefore, the number one one funcitons from the set A to the set B is zero.