AMC10 2005 B
AMC10 2005 B · Q18
AMC10 2005 B · Q18. It mainly tests Basic counting (rules of product/sum), Combinations.
All of David’s telephone numbers have the form 555–abc–defg, where a, b, c, d, e, f, and g are distinct digits and in increasing order, and none is either 0 or 1. How many different telephone numbers can David have?
David 的所有电话号码形式为 555–abc–defg，其中 a, b, c, d, e, f, g 是不同的数字且按升序排列，且都不为 0 或 1。David 可以有多少个不同的电话号码？
(A)
1
1
(B)
2
2
(C)
7
7
(D)
8
8
(E)
9
9
Answer
Correct choice: (D)
正确答案：（D）
Solution
The last seven digits of the phone number use seven of the eight digits ${2, 3, 4, 5, 6, 7, 8, 9}$, so all but one of these digits is used. The unused digit can be chosen in eight ways. The remaining seven digits are then placed in increasing order to obtain a possible phone number. Thus there are 8 possible phone numbers.
电话号码的后七位使用 {2, 3, 4, 5, 6, 7, 8, 9} 中的七个数字，因此漏掉其中一个数字。未使用的数字有 8 种选择。然后剩余的七个数字按升序排列即可得到一个可能的电话号码。因此共有 8 个可能的电话号码。
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