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# An auto assembly plant performs six functions with each frame that arr

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Math Expert
Joined: 02 Sep 2009
Posts: 58453
An auto assembly plant performs six functions with each frame that arr  [#permalink]

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22 Apr 2015, 03:24
2
14
00:00

Difficulty:

85% (hard)

Question Stats:

43% (01:47) correct 57% (01:49) wrong based on 191 sessions

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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

Kudos for a correct solution.

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Re: An auto assembly plant performs six functions with each frame that arr  [#permalink]

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22 Apr 2015, 11:13
5
2
C) 360

short way: there are 6C! ways to do the six tasks. Half will have wheels before axles and half will have axles before wheels. So we want 6C!/2 -> 720/2 = 360
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Re: An auto assembly plant performs six functions with each frame that arr  [#permalink]

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23 Apr 2015, 06:02
2
2
For a discussion on the symmetry principle used to solve this question, check: http://www.veritasprep.com/blog/2011/10 ... s-part-ii/
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Re: An auto assembly plant performs six functions with each frame that arr  [#permalink]

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23 Apr 2015, 09:41
4
I like the Wofford09 answer but for a lengthy solution, here you go...

If Axle can be first job, then rest five job can arranged in 5! ways.

If the Axle is the second job, the Wheel can be done in 4 ways and the remaining 4 jobs can be arranged in 4!.

If the Axle is the third job, the wheel can be done in 3 ways and the reamining 4 jobs can be arranged in 4!.

If the Axle is the second job, the wheel can be done in 2 ways and the reamining 4 jobs can be arranged in 4!.

.....

Finally total permuations.., 5! + (4+3+2+1) 4!= 360 ways.

As soon as I saw the question, I started working on it.... I presume I have a slow a bit to be able to do what wooford09 Did.

Bunuel 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

Kudos for a correct solution.

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Kudos to you, for helping me with some KUDOS.
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Re: An auto assembly plant performs six functions with each frame that arr  [#permalink]

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23 Apr 2015, 09:51
1
shriramvelamuri wrote:
I like the Wofford09 answer but for a lengthy solution, here you go...

If Axle can be first job, then rest five job can arranged in 5! ways.

If the Axle is the second job, the Wheel can be done in 4 ways and the remaining 4 jobs can be arranged in 4!.

If the Axle is the third job, the wheel can be done in 3 ways and the reamining 4 jobs can be arranged in 4!.

If the Axle is the second job, the wheel can be done in 2 ways and the reamining 4 jobs can be arranged in 4!.

.....

Finally total permuations.., 5! + (4+3+2+1) 4!= 360 ways.

As soon as I saw the question, I started working on it.... I presume I have a slow a bit to be able to do what wooford09 Did.

Bunuel 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

Kudos for a correct solution.

I think knowing the lengthy solution is also very important (and a very good exercise to do). Kudos
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Re: An auto assembly plant performs six functions with each frame that arr  [#permalink]

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25 Apr 2015, 12:05
3
2
Bunuel 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

Kudos for a correct solution.

Total number of ways in which the two specific functions can be selected out of the 6 functions=6C2
Remaining 4 functions can be arranged in 4! ways.
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Posts: 58453
Re: An auto assembly plant performs six functions with each frame that arr  [#permalink]

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27 Apr 2015, 04:03
1
2
Bunuel 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

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

C. In this permutations problem (the order does matter - that's what they're asking about!), there are six items to be arranged in order, so the "unrestricted" permutation would be 6! = 720. But there's a catch - since wheels cannot come before axles, any permutation that would put wheels before axles does not work. How do you find that restriction? It's actually a bit simpler than you might think - if you're considering all possibilities, half the time axles will come before wheels (acceptable) and half the time wheels will come before axles (unacceptable). So take away the unacceptable half of the 720 arrangements and 360 are left.
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Re: An auto assembly plant performs six functions with each frame that arr  [#permalink]

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30 Oct 2015, 07:12
Hi there,

I'm not able to quite see why is half before and half after. I understand it, but I can not see it!

Can anyone explain?

Thanks
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Re: An auto assembly plant performs six functions with each frame that arr  [#permalink]

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28 Nov 2016, 22:41
3
1
VeritasPrepKarishma wrote:
For a discussion on the symmetry principle used to solve this question, check: http://www.veritasprep.com/blog/2011/10 ... s-part-ii/

Responding to a pm:

Quote:
Since there are 6 tasks and 2 of them have to performed in a specified order, I grouped them and we get a total of 5 tasks(group of 2 tasks acting as one)
Then I arranged them to get total of 5! ways i.e 120 ways...
Please tell me where I wrong...

Note that axles have to put before wheels but not necessarily immediately before. What I mean to say is that

axles, wheels, windshield, instrument panel, steering wheel, interior seating
is possible and so is
axles, windshield, instrument panel, steering wheel, interior seating, wheels
and also
axles, windshield, instrument panel, wheels, steering wheel, interior seating
etc

The point is, as long as axles come sometime before wheels, it is fine.
When you club them together in a group, you are only allowing case 1.

That is the problem.
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Re: An auto assembly plant performs six functions with each frame that arr  [#permalink]

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27 May 2019, 05:39
The mistake I did was taking
A,W,_,_,_,_ . Now I took A,W as one block & rest others as separate blocks. This gives 5! as answer. But the logic we are missing is the question didn’t say both A,W should happen immediately after one another. It just said that W should happen after A.

So all the possible combinations are:
A,W,_,_,_,_
A,W,_,_,_,_
A,W,_,_,_,_
A,W,_,_,_,_
A,W,_,_,_,_
_,A,W,_,_,_
_,A,_W,_,_
.
.
.
.
_,_,_,_,A,W

If Axle can be first job, then rest five job can arranged in 5! ways.

If the Axle is the second job, the Wheel can be done in 4 ways and the remaining 4 jobs can be arranged in 4!.

If the Axle is the third job, the wheel can be done in 3 ways and the reamining 4 jobs can be arranged in 4!.

If the Axle is the second job, the wheel can be done in 2 ways and the reamining 4 jobs can be arranged in 4!.

.....

Finally total permuations.., 5! + (4+3+2+1) 4!= 360 ways.

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Re: An auto assembly plant performs six functions with each frame that arr  [#permalink]

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19 Aug 2019, 10:53
Total number of ways in which 6 functions can be arranged = 6!

This will have only two types of scenarios involving installation of axles and fitting of wheels.

1. The former can happen before the latter.
2. The latter can happen before the former.

In fact, the number of possible arrangements of both is equal to each other.

Therefore, number of acceptable ways = 6!/2 = 360 ways.
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Re: An auto assembly plant performs six functions with each frame that arr  [#permalink]

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04 Oct 2019, 13:43
KS15 wrote:
Bunuel 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

Kudos for a correct solution.

Total number of ways in which the two specific functions can be selected out of the 6 functions=6C2
Remaining 4 functions can be arranged in 4! ways.

I see that this gives the answer but I don't understand why .

Can you please explain why did you decide to choose 2 specific functions but not bother with arranging them as asked ?
Re: An auto assembly plant performs six functions with each frame that arr   [#permalink] 04 Oct 2019, 13:43
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