Ben and Ann are among 7 contestants from which 4 semifinalists are to be selected. Of the different possible selections, how man

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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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Ben and Ann are among 7 contestants from which 4 semifinalists are to be selected. Of the different possible selections, how man

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