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GRE Math Challenge #16 - Martha invited 4 friends to go with

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GRE Math Challenge #16 - Martha invited 4 friends to go with [#permalink] New post 09 Sep 2014, 01:41
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Question Stats:

100% (01:10) correct 0% (00:00) wrong based on 3 sessions
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?

[Reveal] Spoiler: Answer
24

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Re: GRE Math Challenge #16 - Martha invited 4 friends to go with [#permalink] New post 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?

[Reveal] Spoiler: 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   [#permalink] 23 Sep 2017, 08:56
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