(a) 用数字 $\{1,2,3,4,5,6,7\}$ 可以组成多少个大于 200 的不同三位数，要求数字可以重复使用，且该数能被 5 整除？

(b) 用数字 $\{1,2,3,4,5,6,7\}$ 可以组成多少个大于 200 的不同三位数，要求数字不重复使用，且该数为偶数？

Answer all questions. You should use a calculator where appropriate.

You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.

请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。

能被5整除，个位只能为5；百位不能为1，十位可任取给出的7个数字，因为允许重复。

The units digit must be 5. The hundreds digit has 6 choices, from 2 to 7, and the tens digit has 7 choices. Thus the required number is

先限制最强的个位：只有2、4、6可选。确定个位后，百位从2至7中排除该数字，十位再从剩余数字中选取。

The units digit has 3 choices: 2, 4 or 6.

For each choice, the hundreds digit has 5 choices, since it must be from 2 to 7 and must differ from the units digit. The tens digit then has 5 choices from the remaining digits, including 1.

Therefore the required number is

也可以先按百位的奇偶性分类。百位为偶数会减少个位可选的偶数个数，百位为奇数则不会。

If the hundreds digit is even, it has 3 choices. There are then 2 choices for the even units digit and 5 for the tens digit, giving $3\times2\times5=30$ numbers.

If the hundreds digit is odd, it must be 3, 5 or 7, giving 3 choices. There are 3 choices for the even units digit and 5 for the tens digit, giving $3\times3\times5=45$ numbers.

Hence the required number is