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

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

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.

Check out the blog posts on the link given in my signature below.

I think knowing the lengthy solution is also very important (and a very good exercise to do). Kudos

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)

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.
_________________

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

Responding to a pm:



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.

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.

Posted from my mobile device

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.

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 ?