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permutations and combinations

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by konan » Sun Feb 28, 2016 4:31 am
An auto assembly plant performs six functions with each frame that arrives: add axles, add wheels to the axles, install the windshield to the frame, install the instrument panel, install the steering wheel, and install the interior seating. Once those six tasks are performed, each car goes to a separate building for finishing touches. If these tasks can be arranged along a linear assembly line in any order, except that the axles must be installed before the wheels can be added, how many ways can the assembly line be arranged?
please help me with this...
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by MartyMurray » Sun Feb 28, 2016 4:59 am
konan wrote:An auto assembly plant performs six functions with each frame that arrives: add axles, add wheels to the axles, install the windshield to the frame, install the instrument panel, install the steering wheel, and install the interior seating. Once those six tasks are performed, each car goes to a separate building for finishing touches. If these tasks can be arranged along a linear assembly line in any order, except that the axles must be installed before the wheels can be added, how many ways can the assembly line be arranged?

(A) 120
(B) 240
(C) 360
(D) 480
(E) 720
Six tasks can be arranged the following number of ways.

There are 6 choices for the first task. For each of those 6, there remain 5 that could be chosen second. For each of those 5, there are 4 that could be chosen third, and this pattern continues. So the pattern can be expressed as the following.

6 x 5 x 4 x 3 x 2 x 1 = 720

In this question, there is an additional constraint. The axles must be installed before the wheels can be added. You could get to the answer various ways, such as by first figuring out how many ways the axles and wheels could be set up in order and then adding the rest of the steps. However there is one way that is easiest.

In half of the 720 arrangements the wheels come before the axles and in half the wheels come after. So the answer is 1/2 of 720 = 360.

The correct answer is C.
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by GMATGuruNY » Sun Feb 28, 2016 6:22 am
I posted a solution for a very similar problem here:

https://www.beatthegmat.com/six-mobsters ... 62073.html
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by Matt@VeritasPrep » Tue Mar 01, 2016 11:11 pm
Most seemingly awful combinatorics questions that ask for a lot of different cases have clever (but difficult to find!) solutions like this one, so if you're stuck trying case after case, look for something friendlier.

That said, combinatorics is a pretty small (and odd) part of the GMAT, so don't spend too much time stressing it.
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