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Re: Ann, Mark, Dave and Paula line up at a ticket window. In how many way
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22 Oct 2018, 09:51
Top Contributor
rtaha2412 wrote:
Ann, Mark, Dave and Paula line up at a ticket window. In how many ways can they arrange themselves so that Dave is third in line from the window?
a 24 b 12 c 9 d 6 e 3
Take the task of arranging the 4 people and break it into stages.
We’ll begin with the most restrictive stage.
Stage 1: Select a place in line for Dave Since Dave must be in the 3rd position, we can complete stage 1 in 1 way
Stage 2: Select a place in line for Ann Now that Dave is positioned in line, there are 3 available places remaining. So we can complete stage 2 in 3 ways
Stage 3: Select a place in line for Mark Now that Dave and Ann are positioned in line, there are 2 available places remaining. So we can complete stage 3 in 2 ways
Stage 4: Select a place in line for Paula Now that Mark, Dave and Ann are positioned in line, there is 1 space remaining. So we can complete stage 4 in 1 way
By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus arrange all 4 people) in (1)(3)(2)(1) ways (= 6 ways)
Answer: D
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.