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Sixteen children are trying to decide which two children will win the

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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
[Reveal] Spoiler: OA

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Bunuel wrote:
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


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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Kudos [?]: 2868 [1], given: 364

Sixteen children are trying to decide which two children will win the   [#permalink] 31 Jan 2017, 11:52
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