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  3. 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  23
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 asor). 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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