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Factory X and factory Y are among the 5 factories in a certain manufac

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Factory X and factory Y are among the 5 factories in a certain manufac  [#permalink]

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New post Updated on: 12 Jan 2017, 22:41
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Factory X and factory Y are among the 5 factories in a certain manufacturing business. If the CEO of a business must visit the 5 factories every day, in how many different possible orders can the CEO go to the factories so that factory X is ahead of factory Y?

A. 24
B. 30
C. 36
D. 48
E. 60

Originally posted by Amby02 on 12 Jan 2017, 20:06.
Last edited by Bunuel on 12 Jan 2017, 22:41, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Factory X and factory Y are among the 5 factories in a certain manufac  [#permalink]

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New post 12 Jan 2017, 20:57
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One way to think about the problem:

Without the restriction there would be 5! = 120 ways the factories could be sequenced (you could either use the permutations formula, or use slots: 5 options for the first slot, then, once the first slot is filled, 4 options for the second, then, once the first two slots are filled, three options for the third and so own).

So without the restriction there would be 120 ways.

In half of those 120 ways X will be in front of Y and in the other half Y will be in front of X. (You might think something like: well neither of them is any more likely to be earlier than the other, so half the time X will be earlier and half the time Y will be earlier)

120/2 = 60

So E.
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Re: Factory X and factory Y are among the 5 factories in a certain manufac  [#permalink]

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New post 12 Jan 2017, 22:40
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Hi Amberbajaj02,

This is similar to a question, where it says, There are five persons (A, B, C, D and E) standing in a row, in how many different arrangements person A will be ahead of person B.

As somebody replied above, it’s a symmetrical case, where in half of the total arrangements A would be ahead of B.

So here total arrangements of 5 things, 5! = 120. So In half of the cases he would visit “X” ahead of Y. so that is 60.

So another way of looking at this question is,

There are five slots,

B _ _ _ _ : So here A could be any of the four places, and the remaining three persons can be arranged in 3!. So that is 4 * 3!.

or

_ B _ _ _ : So here A could be any of the three places, and the remaining three persons can be arranged in 3!. So that is 3 * 3!.

or

_ _ B _ _ : So here A could be any of the two places, and the remaining three persons can be arranged in 3!. So that is 2 * 3!.

or

_ _ _ B _ : So here A could be only one place, and the remaining three persons can be arranged in 3!. So that is 1 * 3!.

So, total (4+3+2+1)*3!

10* 3! = 10 * 6 = 60.

So the answer is E.

Hope this is clear.

PS: I still feel that question should have framed better.
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Re: Factory X and factory Y are among the 5 factories in a certain manufac  [#permalink]

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New post 12 Jan 2017, 22:42
amberbajaj02 wrote:
Factory X and factory Y are among the 5 factories in a certain manufacturing business. If the CEO of a business must visit the 5 factories every day, in how many different possible orders can the CEO go to the factories so that factory X is ahead of factory Y?

A. 24
B. 30
C. 36
D. 48
E. 60


Please follow the rules when posting a question: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 1, 3, 9, and 12. Thank you.

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Re: Factory X and factory Y are among the 5 factories in a certain manufac  [#permalink]

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New post 23 Feb 2019, 12:52
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Re: Factory X and factory Y are among the 5 factories in a certain manufac   [#permalink] 23 Feb 2019, 12:52
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