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Carol is having friends over to watch home movies

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Carol is having friends over to watch home movies

by BTGmoderatorDC » Mon Dec 11, 2017 4:01 am
Carol is having friends over to watch home movies. She has 6 reels of home movies, but she and her friends have time to watch only 3 of them. Carol must decide which reels to watch and in what order. How many different orderings does Carol have from which to choose?

A. 120
B. 96
C. 60
D. 36
E. 20

How will i start solving it?

OA A
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by Brent@GMATPrepNow » Mon Dec 11, 2017 7:48 am
lheiannie07 wrote:Carol is having friends over to watch home movies. She has 6 reels of home movies, but she and her friends have time to watch only 3 of them. Carol must decide which reels to watch and in what order. How many different orderings does Carol have from which to choose?

A. 120
B. 96
C. 60
D. 36
E. 20
Take the task of creating the movie playlist and break it into stages.

Stage 1: Select the movie to watch FIRST
There are 6 movies to choose from, so we can complete stage 1 in 6 ways

Stage 2: Select the movie to watch SECOND
There are 5 remaining movies to choose from, so we can complete stage 2 in 5 ways

Stage 3: Select the movie to watch THIRD
There are 4 remaining movies to choose from, so we can complete stage 3 in 4 ways

By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create the movie playlist) in (6)(5)(4) ways (= 120 ways)

Answer: A
--------------------------

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Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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