Question

If $A=\{1,2,3,4,5\},B=\{a,b,c,d\}$, then find the number of possible one-one functions from $A$ to $B$.

Answer 1

One-one functions are possible from $A$ to $B$ when $n\left(A\right)\le n\left(B\right)$

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

Number of possible one-one functions from $A$ to $B$.

${}^{n\left(B\right)}{P}_{n\left(A\right)}=\frac{n\left(B\right)!}{(n\left(B\right)-n\left(A\right))!}$ if $n\left(A\right)\le n\left(B\right)$

$\therefore$Number of possible one-one functions from $A$ to $B$ is $0$