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  3. Ben and Ann are among 7 contestants from which 4 semifinalists are to be selecte

Ben and Ann are among 7 contestants from which 4 semifinalists are to be selecte

游客2024-01-13  64
问题 Ben and Ann are among 7 contestants from which 4 semifinalists are to be selected. Of the different possible selections, how many contain neither Ben nor Ann?
选项 A、5
B、6
C、7
D、14
E、21
答案 A
解析 The number of possible selections of 4 semifinalists that do not contain Ben or Ann is equal to the number of possible selections of 4 semifinalists from the remaining 7-2 = 5 contestants, which is equal to. Alternatively, the number of possible selections of 4 semifinalists from the remaining 5 contestants is equal to the number of possible selections of exactly 1 non-semifinalist, which is equal to 5.
The correct answer is A.
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