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# A plant manager must assign 10 new workers to one of five shifts. She

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Math Expert
Joined: 02 Sep 2009
Posts: 58327
A plant manager must assign 10 new workers to one of five shifts. She  [#permalink]

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19 Aug 2015, 23:28
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Difficulty:

95% (hard)

Question Stats:

46% (02:20) correct 54% (02:48) wrong based on 123 sessions

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A plant manager must assign 10 new workers to one of five shifts. She needs a first, second, and third shift, and two alternate shifts. Each of the shifts will receive 2 new workers. How many different ways can she assign the new workers?

A. 2430
B. 2700
C. 3300
D. 4860
E. 5400

Kudos for a correct solution.

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Re: A plant manager must assign 10 new workers to one of five shifts. She  [#permalink]

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19 Aug 2015, 23:53
2
Bunuel wrote:
A plant manager must assign 10 new workers to one of five shifts. She needs a first, second, and third shift, and two alternate shifts. Each of the shifts will receive 2 new workers. How many different ways can she assign the new workers?

A. 2430
B. 2700
C. 3300
D. 4860
E. 5400

I do not even understand the question...
five shifts and she has 10 workers to assign. She needs first, second and third, and two alternate... what does this line means??
is it means that we need to assign two workers to these shifts or team of two? i am going with the later one.

whatever : my take selecting team of 2 out of 10 to assign to the shifts = 10C2 = 45 ways.

now 2 out of 10 means total of 5 group possible.
so putting them in shifts = counting methode: first, second, third, alt , alt
= 5*4*3*2*1 = 120
here alt and alt are the same: so 120/2 = 60 ways.

total ways of selecting = (selecting 2 out of 10)*arranging those teams in shifts
= 45*60 = 2700

Ans: B
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Math Expert
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Posts: 58327
Re: A plant manager must assign 10 new workers to one of five shifts. She  [#permalink]

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23 Aug 2015, 11:20
Bunuel wrote:
A plant manager must assign 10 new workers to one of five shifts. She needs a first, second, and third shift, and two alternate shifts. Each of the shifts will receive 2 new workers. How many different ways can she assign the new workers?

A. 2430
B. 2700
C. 3300
D. 4860
E. 5400

Kudos for a correct solution.

Economist GMAT Tutor Official Solution:

Let’s begin with our key question: Does order/position matter?

First, note that we don’t have any distinctions between positions on our teams of five. The team made up of Ann and Bob is the same team whether Ann or Bob is picked first, and so on.

Begin with the initial selection, 10 workers selected 2 at a time: 10C2. So, we have:

10!/(2!(10-2)!) = 45.

From our initial 45 possible shifts, we must assign workers to first, second, third, or alternate shift. Here is where order matters. Note, however, that no distinction is made between alternate shifts. So we have three possible assignments per team in which order matters: first, second, or third shift. This is a fairly straightforward permutation problem, but remember that even though you have 5 teams to choose from, only 3 choices matter in terms of order, so 5P3:

5!/(5-3)! = 60.

So, in the end, we have 45 possible team arrangements and 60 ways to select first, second, and third shifts from whichever arrangement is chosen. Our final step is to multiply these two values together to get our answer: 45 x 60 = 2700.
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Re: A plant manager must assign 10 new workers to one of five shifts. She  [#permalink]

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28 Dec 2015, 04:04
Am I right, that if there wouldn't be the constraint with the two indifferent alternative shifts, I would be able to apply the following formula?:
$$\frac{(nm)!}{(n!)^m * m!}$$

n = number of participants in one group
m = number of groups

Thank you very much in advance!
Manager
Joined: 03 May 2013
Posts: 67
Re: A plant manager must assign 10 new workers to one of five shifts. She  [#permalink]

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15 May 2016, 20:37
the stem ihas ambiguity , what about 8 remaining new workers and 4 other remaining shifts, Or are we supposed to arrange only 2 new workers in any shift( as solution does)
Intern
Joined: 31 Aug 2016
Posts: 45
Re: A plant manager must assign 10 new workers to one of five shifts. She  [#permalink]

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01 Jun 2018, 03:10
bump... more analysis?
Intern
Joined: 31 Aug 2016
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A plant manager must assign 10 new workers to one of five shifts. She  [#permalink]

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01 Jun 2018, 03:30
Can someone further explain this? For example why we don't take (10!/8!x2!) x (8!/6!x2!).. which is the classic way to count the ways in which we separate people in teams?

Bunuel VeritasPrepKarishma niks18
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Re: A plant manager must assign 10 new workers to one of five shifts. She  [#permalink]

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01 Jun 2018, 11:44
standyonda wrote:
Can someone further explain this? For example why we don't take (10!/8!x2!) x (8!/6!x2!).. which is the classic way to count the ways in which we separate people in teams?

Bunuel VeritasPrepKarishma niks18

Hi standyonda

This question has two parts to it -

Part 1: You have 10 new members and you need to assign 2 new members to each shift. This is straight forward calculation $$10_C_2$$

Part 2: You have 5 shifts: first, second, third , alternate & alternate i.e 5 groups to arrange 2 new members. But essentially the alternate & alternate are same, hence order does not matter for them, so finally you have 3 orders to arrange the 5 shifts. hence the calculation will be $$5_P_3$$

And in the end we have 45 ways to select 2 team member and 60 ways to select a shift for each team
Re: A plant manager must assign 10 new workers to one of five shifts. She   [#permalink] 01 Jun 2018, 11:44
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