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Martha invited 4 friends to go with her to the movies. There

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Martha invited 4 friends to go with her to the movies. There [#permalink] New post 30 May 2019, 11:21
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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 of 5 seats, one person per seat. In how many of those ways is Martha sitting in the middle seat?


[Reveal] Spoiler: OA
24


Math Review
Question: 7
Page: 297
Difficulty: medium

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Re: Martha invited 4 friends to go with her to the movies. There [#permalink] New post 31 May 2019, 04:33
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Carcass 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 of 5 seats, one person per seat. In how many of those ways is Martha sitting in the middle seat?


[Reveal] Spoiler: OA
24


Math Review
Question: 7
Page: 297
Difficulty: medium


Take the task of seating the 5 people and break it into stages.

We’ll begin with the most restrictive stage.

Stage 1: Select someone to sit in the MIDDLE seat
Since we're told Martha MUST sit in the middle seat, we must place her in that seat.
So, we can complete stage 1 in 1 way

Stage 2: Select someone to sit in seat #1
There are 4 people remaining to be seated, so we can complete this stage in 4 ways

Stage 3: Select someone to sit in seat #2
There are 3 people remaining to be seated, so we can complete this stage in 3 ways

Stage 4: Select someone to sit in seat #4
There are 2 people remaining to be seated, so we can complete this stage in 2 ways

Stage 5: Select someone to sit in seat #5
There is 1 person remaining to be seated, so we can complete this stage in 1 way

By the Fundamental Counting Principle (FCP), we can complete all 5 stages (and thus seat all 5 people) 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 GMAT. So, be sure to learn

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Re: Martha invited 4 friends to go with her to the movies. There   [#permalink] 31 May 2019, 04:33
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Martha invited 4 friends to go with her to the movies. There

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