Question

Number of one-one functions from A to B where $n\left(A\right)=4,n\left(B\right)=5$.

• A. $4$
• B. $5$
• C. $120$
• D. $90$

Answer 1

The correct option is C $120$

$n\left(A\right)=4$ and $n\left(B\right)=5$
For one-one mapping
4 elements can be selected out of 5 elements of set B in ${}^5{C}_4$ ways
and then those 4 selected elements can be mapped with 4 elements of set A in $4!$ ways.
Number of one-one mapping from $A$ to $B$ $={}^5{C}_4\times 4!={}^5{P}_4=\frac{5!}{(5-4)!}=5!=120$