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31 Jan 2017, 10:11
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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71% (01:15) correct
29%
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Sixteen children are trying to decide which two children will win the president and vice-president positions in the class. Each child can and will cast a vote for anyone in the class. If each child in the class is eligible for a position, how many different outcomes are there of the election?
A. 15
B. 30
C. 60
D. 120
E. 240
A. 15
B. 30
C. 60
D. 120
E. 240
31 Jan 2017, 12:52
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Bunuel
Sixteen children are trying to decide which two children will win the president and vice-president positions in the class. Each child can and will cast a vote for anyone in the class. If each child in the class is eligible for a position, how many different outcomes are there of the election?
A. 15
B. 30
C. 60
D. 120
E. 240
A. 15
B. 30
C. 60
D. 120
E. 240
Take the task of selecting a president and vice-president, and break it into stages.
Stage 1: Select someone to be president.
There are 16 children to choose from, so we can complete stage 1 in 16 ways
Stage 2: Select someone to be vice-president.
Once a child has been selected to be president, that child cannot also be vice-president.
So, there are 15 remaining children to choose from, so we can complete stage 2 in 15 ways
By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus select a president and vice-president) in (16)(15) ways (240 ways)
Answer: E
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT so be sure to learn it.
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General Discussion
05 Jul 2018, 16:18
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Quote:
By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus select a president and vice-president) in (16)(15) ways (240 ways)
Why can't we solve it this way? 16c2=120?
