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An engagement team consists of a project manager, team leade

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Re: An engagement team consists of a project manager, team leade  [#permalink]

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New post 20 Jun 2018, 10:27
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marcodonzelli wrote:
An engagement team consists of a project manager, team leader, and four consultants. There are 2 candidates for the position of project manager, 3 candidates for the position of team leader, and 7 candidates for the 4 consultant slots. If 2 out of 7 consultants refuse to be on the same team, how many different teams are possible?

A. 25
B. 35
C. 150
D. 210
E. 300


Given a team is to be formed of 1 PM, 1 TL & 4 consultants, out of 2 candidates for the position of PM, 3 candidates for TL & 7 for consultants.

Constraint is that 2 of the 7 consultants cannot be on same team. Let these 2 be called A & B

We have two cases:

Case 1: Choose one of the 2 consultants ( A or B) & put him on the team & choose the rest 3 from the remaining 5.

We get # of ways as = 2C1 * 5C3 * 2C1 * 3C1 = 2 * (5*4*3/1*2*3) * 2 *3 = 120

Case 2: Exclude both A & B and choose the 4 consultants from the remaining 5 consultants.

We get # of ways as = 5C4 * 2C1 * 3C1 = 5 * 2 * 3 = 30

Hence total # of ways = 120 + 30 = 150

Answer C.


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Re: An engagement team consists of a project manager, team leade  [#permalink]

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New post 20 Jun 2018, 11:14
2 * 3 * Ways of choosing 4 Consultants
Consultant candidates: a b c d e f g
a b not on the same team

either a/b on the team
2 * 1 * 5C3 = 20

neither a b on the team
5C4 = 5

So 25 ways for choosing 4 consultants

2 * 3 * 25 = 150
Answer C
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Re: An engagement team consists of a project manager, team leade  [#permalink]

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New post 06 Jul 2019, 01:36
ASredhar wrote:
marcodonzelli wrote:
An engagement team consists of a project manager, team leader, and four consultants. There are 2 candidates for the position of project manager, 3 candidates for the position of team leader, and 7 candidates for the 4 consultant slots. If 2 out of 7 consultants refuse to be on the same team, how many different teams are possible?

A. 25
B. 35
C. 150
D. 210
E. 300


This is how I solved this question and got the answer incorrect.

Total Combinations - (the number of combinations in which A and B are always together) = Number of ways in which A and B won't work together

Assuming that A and B are the two consultants who don't want to work together.

Number of ways to choose 1 PM out of 2 candidates x Number of ways to choose 1 TL out of 3 candidates x Number of ways to choose 4 Consultants out of 7 candidates = Total

2 ways x 3 ways x 35 ways(7!/4!.3!) = 210 ways.

I got this right. However, somewhere in the next steps is where I made a mistake.

Number of ways in which A and B will work together and the rest two positions can be filled with the remaining 5 candidates.

2 x 3 x 1 x 1 x 5 x 4

So I subtracted 120 from 210.

However after following the answers here, I understood that for the remaining two positions, instead of doing a 5C2, I chose to fill them in 5 ways and 4 ways.

I would like to understand: 1) what sort of an error am I committing. 2When should I follow the approach I used above and when should I do a 5C2 logic.

Suggestions welcome. Thanks!

Regards,
Arvind.



Hi Arvind,

I had the same query, but the concept of ordered and unordered selections helped me clear that doubt.

when we choose to us 5 x 4 to select the remaining two, it implies that the order of selection is important, whereas, when we use the formula 5C2 it implies that the order of selection is unimportant.

Which is what brings the difference in the answer. For this particular problem, the order of selection is unimportant and therefore the formula 5C2 will yield the correct answer.


Hope that helps!
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Re: An engagement team consists of a project manager, team leade  [#permalink]

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New post 02 Aug 2019, 02:40
Hi! Can someone please explain what is wrong with this approach :
2c1 * 3c1 * 5c3 * 2c1 ( 5c3 = 5 without issues consultants for 3 positions and 2c1 = 2 consultants who have problem have only spot)
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Re: An engagement team consists of a project manager, team leade  [#permalink]

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New post 02 Aug 2019, 13:38
Hi kunalbean,

Your calculation assumes that 1 of the 4 "consultant" spots must be taken by 1 of the 2 candidates who will not work with one another. However, it's possible that NEITHER of those 2 candidates are selected for those 4 spots - so you have to account for those additional options.

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Re: An engagement team consists of a project manager, team leade  [#permalink]

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New post 02 Aug 2019, 14:48
EMPOWERgmatRichC wrote:
Hi kunalbean,

Your calculation assumes that 1 of the 4 "consultant" spots must be taken by 1 of the 2 candidates who will not work with one another. However, it's possible that NEITHER of those 2 candidates are selected for those 4 spots - so you have to account for those additional options.

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Thank you for the response! One quick question - As you've got 800 - how can one ensure of thinking through all the possibilities ? for example, in this case, the one you stated above.
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Re: An engagement team consists of a project manager, team leade  [#permalink]

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New post 03 Aug 2019, 14:31
Hi kunalbean,

Consistent and proper note-taking is one of the 'keys' to maximizing your Score on Test Day, so when you're facing a situation in which you have to think about more than one possible outcome, you would almost certainly find it helpful to take some quick notes on what outcomes are. Sometimes the simple act of writing out ideas that you already know can get you thinking about other aspects of the question (especially those that you might not have considered).

For example, in this prompt, you might write down:

PM: 2 possibilities
TM: 3 possibilites
Consultants: 7 possible (A,B,C,D,E,F,G), choose 4 - A and B CANNOT be on the team together.

That last bit is especially important: it does NOT state "choose A or B"... it states "those 2 can't be on the team together." There's nothing in the prompt that states that one of them 'must' be on the team, so logic dictates that we have to consider that possibility.
.
.
A and 3 of 5 others
B and 3 of 5 others
Neither and 4 of the other 5

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Re: An engagement team consists of a project manager, team leade   [#permalink] 03 Aug 2019, 14:31

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