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A certain company assigns employees to offices in such a way [#permalink]
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 08 Jan 2010, 14:18
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A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices? A. 5 B. 6 C. 7 D. 8 E. 9
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Re: A certain company [#permalink]
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08 Jan 2010, 16:58
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Re: A certain company [#permalink]
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09 Jan 2010, 03:27
i am still not able to understand. Can you please explain in detail?
also please tell me where i went wrong.This was my logic.
No. of people
office 1: 0|0|0|1|1|1|2|2|3
office 2: 1|2|3|0|1|2|0|1|0
this gives me 9 possible combination
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Re: A certain company [#permalink]
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09 Jan 2010, 04:25
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sagarsabnis wrote: i am still not able to understand. Can you please explain in detail?
also please tell me where i went wrong.This was my logic.
No. of people
office 1: 0|0|0|1|1|1|2|2|3
office 2: 1|2|3|0|1|2|0|1|0
this gives me 9 possible combination First of all you should assign ALL 3 employees to either of the offices. You can have the following scenarios: No. of people ***********A|B|C|D| office 1: 0|1|2|3| office 2: 3|2|1|0| In scenario (A) and (D) there is only one way to assign three people. But in (B) and (C) there will be 3 cases in each: Let's say there are 3 employees: Tom, Mary and Kate. In (B): Tom can be in office #1 and Mary/Kate in #2 OR Mary can be in #1 and Tom/Kate in #2 OR Kate in #1 and Tom/Mary in #2. Total 3 cases for (B). The same for (C). (A)+(B)+(C)+(D)=1+3+3+1=8. The way I solved this was different: Each of the three employees, Tom, Mary and Kate, has two choices office #1 or office #2. Hence total # of combinations (assignments) is 2*2*2=2^3=8. Hope it's clear.
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Re: A certain company employee [#permalink]
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25 Oct 2010, 04:26
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Two offices can be filled in two ways, when all the three employee will be in same room or when two employee in one room and one in other room.
when all the three employee will be in same = 3C3 * 2! =2 (2!, because any of the room can be taken)
when two employee in one room and one in other room. = 3C2 * 1C1 * 2! = 6
Hence total ways = 6+2
Answer is 8.
Consider KUDOS if it is helpful to u.
Last edited by ankitranjan on 25 Oct 2010, 04:43, edited 1 time in total.
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Re: A certain company employee [#permalink]
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25 Oct 2010, 04:38
monirjewel wrote: A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office, In how many ways can the company assign 3 employees to 2 different offices?
A) 5
B) 6
C) 7
D) 8
E) 9 Every employee has got the possibilit of getting assigned to any of the two offices. Hence total possibilities = 2^3 = 8
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Re: Why D any not B? please help me out [#permalink]
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17 Nov 2010, 08:56
SoniaSaini wrote: A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices?
A. 5
B. 6
C. 7
D. 8
E. 9
thanks in advance!!! For each one of the 3 employees, there are two choices. He can be allotted to any one of the two offices. Hence total number ways will be 2 * 2* 2 = 8 ways
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Re: A certain company [#permalink]
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21 Nov 2010, 07:12
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The best way to remember this is :
(Decisions) ^ (Players)
For this problem - 2 decisions , 3 players : 2^3=8
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Re: Specific GMAT Question [#permalink]
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01 Oct 2012, 13:13
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Re: A certain company assigns employees to offices in such a way [#permalink]
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06 Jul 2013, 17:59
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Thank you. Then, if the company assigns employees to offices in such a way that if the offices can not be empty and more than one employee can be assigned to an office. And we have 5 employees and 3 rooms, the answer would be: 120? I mean, 5!
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Re: A certain company assigns employees to offices in such a way [#permalink]
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Re: A certain company assigns employees to offices in such a way [#permalink]
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07 Jul 2013, 13:35
Thank you Bunuel! I have difficulties learning combinations, this is my weakest area in the GMAT. I am planning to practice all the combinations problems in the forum. Regarding the problem that I have posted before, I think that you mean: \(3^5\) - the combinations in which zero is an element in the set and it cannot be zero in any of the slots, with the restrictions that the 3 elements must sum up 5): {(005),(014),(023),(032),(041) ; (050)(140),(230),(320),(410) ; (500),(104),(203),(302),(401)} 243 - 15 = 228 I tried to apply combinatorics formulas to this problem (because writing that set is very time consuming) but I could not figure it out. Translating the problem: I need to find the number of combinations of three digits in which at least one of the digits is "0", the sum of those three digits is 5 and the digits range from 0 to 5 (six elements). Then, substract this number from \(3^5\)
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Re: A certain company assigns employees to offices in such a way [#permalink]
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10 Jul 2013, 12:40
Applying combinations I think would be in this way: \(C^4_1 * C^2_1 = 4*2 = 8\)
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Re: A certain company assigns employees to offices in such a way [#permalink]
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31 Aug 2013, 07:47
ok, can someone tell me what's wrong with my thinking.. 1st office can have any 3 employees.. therefore 3 options, 2nd office can also have any of 3 employees hence again 3 options so it should be 3*3=9 i think the logic is similar to the way Bunuel did..the only difference is in that case we had 2 choices for each employee therefore it was 2*2*2=8.. but why is the answer different in both cases?
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Re: A certain company assigns employees to offices in such a way [#permalink]
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03 Sep 2013, 06:42
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Re: A certain company assigns employees to offices in such a way [#permalink]
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Re: A certain company assigns employees to offices in such a way [#permalink]
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Re: A certain company assigns employees to offices in such a way [#permalink]
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18 Apr 2016, 12:28
Three people that can go in either office 1 or 2 So 2^3 =8 Important is to see that you are not distributing offices to people. That would be 3^2 instead of 2^3
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A certain company assigns employees to offices in such a way [#permalink]
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18 Apr 2016, 15:46
with 2 offices and 3 employees, there are 3 ways to have one's own office, 3 ways to share an office with one other, and 2 ways to share an office with two others, or 8 ways total
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Re: A certain company assigns employees to offices in such a way [#permalink]
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08 Aug 2016, 10:32
For 2 employees in 1 office and the other alone: it should be 3 C 1 x 2 (since we only have to choose 1 out of three who will be alone) and then multiply by 2 since there are two offices?
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Re: A certain company assigns employees to offices in such a way
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08 Aug 2016, 10:32
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