Let  $A=\{(x,y);2x+3y=23;x,y\in N\}$  and   $B=\{x:(x,y)\in A\}$  ,then the number of one-one functions from A to B  is equals 

$$\begin{gathered} 2x+3y=23:x_{1}y\in N (x,y)=(1,7),(4,5),(7,3),(10,1) \\ \therefore A=\{(1,7),(4,5),(7,3),(10,1)\} B=\{1,4,7,10\} \\ \therefore \mathrm{number} \mathrm{of} \mathrm{one} \mathrm{ne} \mathrm{function} \mathrm{from} \\ A\mathrm{to} B in 4!=24 \end{gathered}$$