Question

Consider set $A=1,2,3,4$ and set $B=0,2,4,6,8$, then the number of one-one function from set $A$ to set $B$ is ?

• A. $5$
• B. $24$
• C. $120$
• D. None of these

Answer 1

The correct option is C $120$

Number of one-one function from

$\underset{\left(m\right)}{A}$ to $\underset{\left(n\right)}{B}=\{\begin{array}{cc}{}^n{P}_m,& ifn\ge m\\ 0,& ifn<m\end{array}$

$m=4,n=5$

One-one function $={}^5{P}_4=\frac{5!}{1!}=120$