How many possible ordered pairs ( $A, B$ ) of digits are there for which the decimal number

$\large 7\ A\ 8 \ B$ is divisible by 45?

3
0
2
4
1

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The ordered pair is $(3,0)$ and $(7,5)$ . The number is divisible by $5$ and $9$ , so $B$ must be $0$ or $5$ , and the sum of the digits must be divisible by $9$ .