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Let $A=\{(x, y): 2 x+3 y=23, x, y \in \mathbb{N}\}$ and $B=\{x:(x, y) \in A\}$. Then the number of one-one functions from $A$ to $B$ is equal to _______
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The correct answer is:
24
$\begin{array}{ll}
2 x+3 y=23 \\
x=1 & y=7 \\
x=4 & y=5 \\
x=7 & y=3 \\
x=10 & y=1 \\
A & B \\
(1,7) & 1 \\
(4,5) & 4 \\
(7,3) & 7 \\
(10,1) & 10
\end{array}$
The number of one-one functions from $A$ to $B$ is equal to 4 !
2 x+3 y=23 \\
x=1 & y=7 \\
x=4 & y=5 \\
x=7 & y=3 \\
x=10 & y=1 \\
A & B \\
(1,7) & 1 \\
(4,5) & 4 \\
(7,3) & 7 \\
(10,1) & 10
\end{array}$
The number of one-one functions from $A$ to $B$ is equal to 4 !
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