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

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

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New post 22 Apr 2015, 03:24
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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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New post 25 Apr 2015, 12:05
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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.
Answer=6C2*4!=360 (C)
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Re: An auto assembly plant performs six functions with each frame that arr  [#permalink]

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New post 22 Apr 2015, 11:13
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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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New post 23 Apr 2015, 06:02
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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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New post 23 Apr 2015, 09:41
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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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New post 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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New post 27 Apr 2015, 04:03
1
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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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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New post 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?

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

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New post 28 Nov 2016, 22:41
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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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