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Martha invited 4 friends to go with her to the movies. There [#permalink]
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?
Re: Martha invited 4 friends to go with her to the movies. There [#permalink]
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?
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]
04 Oct 2019, 11:16
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?
Re: Martha invited 4 friends to go with her to the movies. There [#permalink]
04 Oct 2019, 17:13
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Asmakan wrote:
How can we solve this question by permutation? \(\frac{n!}{(n-k)!}\)
There are very few "true" permutation questions on the GRE.
The Fundamental Counting Principal is a far more useful counting strategy.
Cheers, Brent
_________________
Brent Hanneson – Creator of greenlighttestprep.com If you enjoy my solutions, you'll like my GRE prep course. Sign up for GRE Question of the Dayemails
Re: Martha invited 4 friends to go with her to the movies. There [#permalink]
13 Oct 2019, 09:13
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Asmakan wrote:
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?
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