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  3. Each person at a party shook hands exactly once with each of the other people at

Each person at a party shook hands exactly once with each of the other people at

游客2024-01-12  68
问题 Each person at a party shook hands exactly once with each of the other people at the party. There was a total of 21 handshakes exchanged at the party.

Column A                                       Column B
The number of people at the party              8
选项 A、if the quantity in Column A is greater
B、if the quantity in Column B is greater
C、if the two quantity are equal
D、if the relationship cannot be determined from the information given
答案 B
解析 参加某次舞会中的每个人都与其他的所有与会者刚好握一次手。在这个舞会中共有21次握手。
解：本题的正确答案为(B)。设出席舞会的人数为n，则握手的总次数=n!/[2! (n-1)!]=n(n-1)/2=21  so, n2-n-42=0。解二次方程可得，n=-6或n=7，舍去负根得出席这次舞会的人数为7。
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