题目信息
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?
A:5
B:6
C:7
D:14
E:21
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正确答案：
A:5
Arithmetic Elementary combinatorics
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
= 5. 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.
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
= 5. 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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