Ann, Mark, Dave and Paula line up at a ticket window. In how many way

Question

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

praveen192 · Accepted Answer

We can fix the position of Dave on the third spot and the others can then be arranged in 3! ways.
3! = 3*2*1 = 6
Hence option D is correct.

Fijisurf · Answer

D

Dave's position is fixed. Now we need to arrange all others around Dave.
There are 3x2x1= 6 ways to arrange three people.

BrentGMATPrepNow · Answer

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.

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fskilnik · Answer

?\,\,\,:\,\,\,{	ext{# }}\,\,{	ext{ways}}\,\,{	ext{with}}\,\,{	ext{Dave position}}\,\,{	ext{fixed}}

We may consider Dave does not "exist": put Ann, Mark and Paula in line (at the 3 positions available to them)!

? = {P_3} = 3! = 6

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
Fabio.

bumpbot · Answer

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Ann, Mark, Dave and Paula line up at a ticket window. In how many way

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Ann, Mark, Dave and Paula line up at a ticket window. In how many way

Prep Toolkit

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