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A courier company can assign its employees to its offices in such a wa

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New post 02 Oct 2018, 02:21
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Question Stats:

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A courier company can assign its employees to its offices in such a way that one or more of the offices can be assigned no employee to all the employees. In how many ways can the company assign four employees to two different offices?

(A) 6
(B) 8
(C) 10
(D) 12
(E) 16

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Re: A courier company can assign its employees to its offices in such a wa  [#permalink]

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New post 04 Oct 2018, 12:43
how many ways can the company assign four employees to two different offices??

A has 2 choices office 1 or office 2
B has 2 choices office 1 or office 2
C has 2 choices office 1 or office 2
D has 2 choices office 1 or office 2

Since this is a dependent Event... you would have to multiply
\(2*2*2*2=16\)
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New post 04 Oct 2018, 14:40
Bunuel wrote:
A courier company can assign its employees to its offices in such a way that at one or more of the offices can be assigned no employee to all the employees. In how many ways can the company assign four employees to two different offices?

(A) 6
(B) 8
(C) 10
(D) 12
(E) 16

Hi, Bunuel ,

I suggest changing the wording (perhaps) to this:

Quote:
A courier company can assign its employees to its offices in such a way that at most one of the offices can be empty (assigned to no employees). In how many ways can the company assign four employees to two different offices?

Reason: the way originally presented, I thought we could let both two offices empty (eventually assigning the employees to other offices).
AvidDreamer09´s solution is coherent to the modification suggested.

Regards,
Fabio.
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Re: A courier company can assign its employees to its offices in such a wa  [#permalink]

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New post 04 Oct 2018, 22:33
fskilnik wrote:
Bunuel wrote:
A courier company can assign its employees to its offices in such a way that at one or more of the offices can be assigned no employee to all the employees. In how many ways can the company assign four employees to two different offices?

(A) 6
(B) 8
(C) 10
(D) 12
(E) 16

Hi, Bunuel ,

I suggest changing the wording (perhaps) to this:

Quote:
A courier company can assign its employees to its offices in such a way that at most one of the offices can be empty (assigned to no employees). In how many ways can the company assign four employees to two different offices?

Reason: the way originally presented, I thought we could let both two offices empty (eventually assigning the employees to other offices).
AvidDreamer09´s solution is coherent to the modification suggested.

Regards,
Fabio.



I'm not sure if my thinking is right. I thought that too. I thought both the offices could be empty but I reasoned 3^4 was not part of the answer choices and well it would be a pointless exercise for the management to not allocate any employee to neither of the office. So I considered 2^4

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New post 05 Oct 2018, 03:18
My answer would be 3^4, too.

Rethinking about the original question stem, now I understand the issue better. The "problem" is that the first sentence does not take into account there are only 2 offices (yet)...

I guess the wording should be changed. My (better) suggestion is the following:

Quote:
In how many ways can a courier company assign four employees to two different offices, if it is possible to have one office empty when all four employees are assigned to the other?

Regards,
Fabio.
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Re: A courier company can assign its employees to its offices in such a wa  [#permalink]

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New post 06 Oct 2018, 22:46
I don't know if my reasoning is correct here, I'd appreciate the critique.

I solved this problem just like the chocolate distribution problem you see here: https://gmatclub.com/forum/in-how-many-ways-5-different-chocolates-be-distributed-to-4-children-231187.html

1 room could go to: 1 emp, 2 emp, 3 emp or 4 emp -- 4 ways

2 rooms, so 4*4= 16
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Re: A courier company can assign its employees to its offices in such a wa  [#permalink]

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New post 06 Oct 2018, 23:25
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Bunuel wrote:
A courier company can assign its employees to its offices in such a way that one or more of the offices can be assigned no employee to all the employees. In how many ways can the company assign four employees to two different offices?

(A) 6
(B) 8
(C) 10
(D) 12
(E) 16


This is how I read this question:

The company has to assign four employees to two different offices. There is no problem if an office has "no employees" or "all employees" or "anything in between".
But the employees HAVE to be assigned to an office.

So each employee has 2 options.
So for 4 employees, we have 2*2*2*2 = 16 options
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New post 07 Oct 2018, 04:28
shaarang wrote:
I don't know if my reasoning is correct here, I'd appreciate the critique.

I solved this problem just like the chocolate distribution problem you see here: https://gmatclub.com/forum/in-how-many-ways-5-different-chocolates-be-distributed-to-4-children-231187.html

1 room could go to: 1 emp, 2 emp, 3 emp or 4 emp -- 4 ways

2 rooms, so 4*4= 16


Hi, shaarang.

In AvidDreamer09´s solution (he certainly meant "INdependent", but I prefer the Fundamental Principle of Counting to justify those multiplications)
and also in Karishma´s solution there is an implicit restriction that any given employee must be assign to exactly one of the two offices.

In your suggestion, it would be
> possible that some employees were assigned to both offices
> possible that some employees were not assigned to any of the 2 offices
> impossible to have an "empty" office (without employees assign to it)

I hope this is "the critique" you asked.

Regards,
Fabio.
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