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GRE Math Challenge #16 - Martha invited 4 friends to go with
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09 Sep 2014, 01:41
09 Sep 2014, 01:41
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88% (00:52) correct
11% (01:25) wrong based on 27 sessions
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Martha invited 4 friends to go with her to the movies. There are 120 different ways in which they can sit together in a row. In how many of those ways is Martha sitting in the middle?
Show: :: Answer
24
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Re: GRE Math Challenge #16 - Martha invited 4 friends to go with
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23 Sep 2017, 08:56
23 Sep 2017, 08:56
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sandy wrote:
Martha invited 4 friends to go with her to the movies. There are 120 different ways in which they can sit together in a row. In how many of those ways is Martha sitting in the middle?
Show: :: Answer
24
Take the task of seating the 5 people and break it into stages.
We’ll begin with the most restrictive stage.
Stage 1: Seat Martha
Since Martha must sit in the middle, we can complete stage 1 in only 1 way
ASIDE: Let A, B, C and D represent Martha's 4 friends
Stage 2: Seat friend A
There are 4 empty chairs to choose from.
So we can complete stage 2 in 4 ways
Stage 3: Seat friend B
There are now 3 empty chairs remaining.
So we can complete stage 3 in 3 ways
Stage 4: Seat friend C
There are now 2 empty chairs remaining.
So we can complete stage 4 in 2 ways
Stage 5: Seat friend C
There is 1 empty chair remaining.
So we can complete stage 5 in 1 way
By the Fundamental Counting Principle (FCP), we can complete all 5 stages (and thus seat all 5 children) in (1)(4)(3)(2)(1) ways (= 24 ways)
Answer: 24
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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Re: GRE Math Challenge #16 - Martha invited 4 friends to go with
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16 Feb 2020, 18:11
16 Feb 2020, 18:11
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This is an official question , located here https://gre.myprepclub.com/forum/martha-in ... 13745.html
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