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Twelve runners enter a race to compete for first, second, an
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30 Dec 2017, 14:30
30 Dec 2017, 14:30
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Question Stats:
80% (00:25) correct
20% (00:34) wrong based on 40 sessions
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Twelve runners enter a race to compete for first, second, and third place. How many different combinations of winners are possible?
Drill 2
Question: 10
Page: 564
Question: 10
Page: 564
Show: :: OA
1320
Re: Twelve runners enter a race to compete for first, second, an
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12 Jan 2018, 15:28
12 Jan 2018, 15:28
Expert Reply
Explanation
In this case, order matters, so you simply need to multiply the number of possible runners for each spot. That should look like this: \(12 \times 11 \times 10 = 1,320\).
In this case, order matters, so you simply need to multiply the number of possible runners for each spot. That should look like this: \(12 \times 11 \times 10 = 1,320\).
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Twelve runners enter a race to compete for first, second, an
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13 Dec 2019, 11:05
13 Dec 2019, 11:05
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sandy wrote:
Twelve runners enter a race to compete for first, second, and third place. How many different combinations of winners are possible?
Drill 2
Question: 10
Page: 564
Question: 10
Page: 564
Show: :: OA
1320
ASIDE: I'm somewhat surprised that this official practice question is somewhat ambiguous. It suggests that the " winners" are the runners who finish first second or third.
Take the task of listing possible winners and break it into stages.
Stage 1: Select a runner to be first
Since there are 12 runners to choose from, we can complete stage 1 in 12 ways
Stage 2: Select a runner to be second
Since we already chose a first place runner in stage 1, there are 11 runners REMAINING to choose from.
So we can complete stage 2 in 11 ways
Stage 3: Select a runner to be 3rd
There are now 10 runners remaining, so we can complete stage 3 in 10 ways
By the Fundamental Counting Principle (FCP), we can complete all 3 stages (list the arrangements of winners) in (12)(11)(10) ways (= 1320 ways)
Answer: 1320
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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