Even numbers, distinct digits

How many $4$ -digit numbers (from $1000$ to $9999$ ) have all four digits distinct and are even?

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Split on whether the last (units) digit is $0$ or a nonzero even — the leading digit's count differs.
$9\cdot 8\cdot 7$ (units $=0$ ) plus $4\cdot 8\cdot 8\cdot 7$ (units $\in\{2,4,6,8\}$ ).

Answer

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2296

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