Let $A=\{(x, y): 2 x+3 y=23, x, y \in N\}$ and $\mathrm{B}=\{\mathrm{x}:(\mathrm{x}, \mathrm{y}) \in \mathrm{A}\}$. Then the number of one-one functions from A to B is equal to
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Solution
$\begin{aligned} & 2 x+3 y=23 \\ & x=1 y=7 \\ & x=4 y=5\end{aligned}$
$
\begin{aligned}
& x=7 y=3 \\
& x=10 \quad y=1
\end{aligned}
$
The number of one-one functions from $A$ to $B$ is equal to 4 !
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