2007 AMC 10A 第 12 题

Question

两名导游带领六名游客。导游决定分开行动。每名游客必须选择其中一名导游，但每名导游至少要带一名游客。导游和游客的不同分组共有多少种？

Two tour guides are leading six tourists. The guides decide to split up. Each tourist must choose one of the guides, but with the stipulation that each guide must take at least one tourist. How many different groupings of guides and tourists are possible?

56

58

60

62

64

答案：D

知识点：乘法原理补集计数

难度评级：1330

小提示：

六名游客各自独立选择两名导游之一。

Each of the six tourists independently picks one of the two guides

大提示：

减去某名导游没有游客的两种安排。

Subtract the two arrangements in which a guide ends up with no tourists

解答：

每名游客独立选择两名导游之一，共有

2^6 = 64

种安排。

其中恰好有两种安排会让某名导游没有游客，所以答案为

64 - 2 = 62

。

所以正确答案是 D。

Each tourist independently chooses one of the two guides, giving

2^6 = 64

arrangements.

Exactly two of these leave a guide with no tourists, so the answer is

64 - 2 = 62.

Thus, the correct answer is D.

2007 AMC 10A 第 12 题

答案：D

难度评级：1330

小提示：

大提示：

解答：

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