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Sixteen children are trying to decide which two children will win the
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06 Oct 2021, 09:13
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Question Stats:
76% (00:45) correct
23% (01:09) wrong based on 13 sessions
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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?
Sixteen children are trying to decide which two children will win the
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06 Oct 2021, 09:21
1
Solution:
No. of ways a president can be select is 16. As, there are 16 children from whom a president can be selected. Thus, 16 ways No. of ways a vice-president can be selected is 15. As one child is already selected as the president. Thus 15 children are left.
Therefore, Number of different outcomes to select President and vice-president= 16x15=240 ways. IMO E
Sixteen children are trying to decide which two children will win the
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06 Oct 2021, 09:24
1
Carcass 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 GRE so be sure to learn it.
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