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A university needs to select a nine-members committe...

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by swerve » Sun Jan 21, 2018 7:31 am
A university needs to select a nine-members committee on extracurricular life, whose members must belong either to the student government or to the student advisory board. If the student government consists of 10 members, the student advisory board consists of 8 members and 6 students hold membership in both organizations, how many different committee are possible?

A. 72
B. 110
C. 220
D. 720
E. 1096

The OA is C.

Please, can any expert explain this PS question for me? I would like to know how to solve it in less than 2 minutes. I need your help. Thanks.
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by [email protected] » Sun Jan 21, 2018 10:59 am
Hi swerve,

We're told that a university needs to select a nine-members committee on extracurricular life, whose members must belong either to the student government or to the student advisory board. The student government consists of 10 members, the student advisory board consists of 8 members and 6 students hold membership in BOTH organizations. We're asked for the number of different nine-member committees that are possible.

To start, we have to determine the total number of people between the 2 groups (since some of those people have been 'counted' twice). Since 6 people are in BOTH groups, the actual total number of people is 10+8-6 = 12. Choosing a group of 9 from a total of 12 requires the Combination Formula:

12c9 = 12! / (9!)(3!) = (12)(11)(10) / (3)(2)(1) = (2)(11)10) = 220 different groups of nine people

Final Answer: C

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by Jeff@TargetTestPrep » Tue Jan 23, 2018 9:15 am
swerve wrote:A university needs to select a nine-members committee on extracurricular life, whose members must belong either to the student government or to the student advisory board. If the student government consists of 10 members, the student advisory board consists of 8 members and 6 students hold membership in both organizations, how many different committee are possible?

A. 72
B. 110
C. 220
D. 720
E. 1096
The number of students who belong either to the student government or to the student advisory board or both is:

Total = # Government + # Advisory - # Both + # Neither

10 + 8 - 6 + 0 = 12 students.

So the number of ways to select the 9-member committee out of 12 possible candidates is 12C9:

12!/[(12-9)! x 9!]

12!/(3! x 9!) = (12 x 11 x 10)/3! = (12 x 11 x 10)/(3 x 2) = 2 x 11 x 10 = 220

Answer: C

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