Question

If $A=\{1,3,5,7\}$ and $B=\{1,2,3,4,5,6,7,8\}$ then the number of one-to-one functions from $A$ into $B$ is

• A. 1340
• B. 1860
• C. 1430
• D. 1880
• E. 1680

Answer 1

The correct option is E 1680

Given, $A=\{1,3,5,7\}$
and $B=\{1,2,3,4,5,6,7,8\}$
Here, $n\left(A\right)=4$ and $n\left(B\right)=8$
Thus number of one-one function from $A$ into $B$
$={}^8{P}_4=\mathrm{8.7.6.5}=1680$