AMC10 2022 B

AMC10 2022 B · Q3

AMC10 2022 B · Q3. It mainly tests Basic counting (rules of product/sum), Casework.

How many three-digit positive integers have an odd number of even digits?

有多少个三位正整数具有奇数个偶数数字？

(A) 150 150

(B) 250 250

(D) 450 450

(E) 550 550

Answer

Correct choice: (D)

正确答案：（D）

Solution

We use simple case work to solve this problem. Case 1: even, even, even = $4 \cdot 5 \cdot 5 = 100$ Case 2: even, odd, odd = $4 \cdot 5 \cdot 5 = 100$ Case 3: odd, even, odd = $5 \cdot 5 \cdot 5 = 125$ Case 4: odd, odd, even = $5 \cdot 5 \cdot 5 = 125$ Simply sum up the cases to get your answer, $100 + 100 + 125 + 125 = \boxed{\textbf{(D)~}450}$.

我们使用简单分类讨论来解决这个问题。情况1：偶、偶、偶 = $4 \cdot 5 \cdot 5 = 100$ 情况2：偶、奇、奇 = $4 \cdot 5 \cdot 5 = 100$ 情况3：奇、偶、奇 = $5 \cdot 5 \cdot 5 = 125$ 情况4：奇、奇、偶 = $5 \cdot 5 \cdot 5 = 125$ 简单相加得到答案，$100 + 100 + 125 + 125 = \boxed{\textbf{(D)~}450}$。

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