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

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Math Expert
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02 Oct 2018, 02:21
00:00

Difficulty:

75% (hard)

Question Stats:

45% (01:46) correct 55% (01:50) wrong based on 122 sessions

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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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04 Oct 2018, 12:43
1
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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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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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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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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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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06 Oct 2018, 23:25
2
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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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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Re: A courier company can assign its employees to its offices in such a wa  [#permalink]

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20 Oct 2018, 01:21
Why cant we use the formula for dividing n identical items between r persons here? n+r-1Cr-1
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Re: A courier company can assign its employees to its offices in such a wa  [#permalink]

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02 Nov 2018, 13:59
Hi all,
I solved it in the following way:
Two offices for four employees and each office can have 0 to four employees.
Now Imagine there are two columns O1 and O2 representing the offices and there are the the following possibilities for allocation.Also note that in each office order doesn't matter ; all that counts is who all I am selecting for first office and thereby implying that the selection for the other office is already done.In other words if I select for O1 a certain set of people then the remaining people will automatically be selected to O2.Now let's consider the possibilities.
1)O1 : 0 people,O2 : 4 people
Number of ways of doing this is only one.note that order doesn't matter
2)O1 : 1 person O2: remaining 3 people
First let's select for O1 there are 4C1 ways and each way O2 people automatically gets selected
3)O1: 2 people O2 remaining 2 people
4C2 ways notice O2 automatically gets selected.

In this ways all cases are ored as 1 + 4C1 + 4C2 + 4C3 + 4C4 + 1 = 16 ways

Notice in each case I am considering the following for O 1 and O2 : 0,4. 1,3. 2,2. 3,1. 4,0.

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Re: A courier company can assign its employees to its offices in such a wa   [#permalink] 02 Nov 2018, 13:59
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