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A manager is forming a 6-person team to work on a certain project. From the 11 c
A manager is forming a 6-person team to work on a certain project. From the 11 c
游客
2025-02-24
31
管理
问题
A manager is forming a 6-person team to work on a certain project. From the 11 candidates available for the team, the manager has already chosen 3 to be on the team. In selecting the other 3 team members, how many different combinations of 3 of the remaining candidates does the manager have to choose from?
选项
A、6
B、24
C、56
D、120
E、462
答案
C
解析
To determine the number of different combinations of 3 of the remaining candidates that the manager has to choose from, you first have to know the number of remaining candidates. Since you know that the manager has already chosen 3 of the 11 candidates to be on the team, it is easy to see that there are 8 remaining candidates. Now you need to count how many different combinations of 3 objects can be chosen from a group of 8 objects.
If you remember the combinations formula, you know that the number of combinations is
(which is denoted symbolically as
or
). You can then calculate the number of different combinations of 3 of the remaining candidates as follows.
The correct answer is Choice C.
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