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Quote:
There are 12 coworkers who work on projects in teams. Each team is composed of 3 people. Each worker is on one and only one team. How many unique teams can be created?

(A) 4
(B) 12
(C) 220
(D) 660
(E) 1,320

12C3=220

Ans (C)
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Can anyone explain the answer here ?
Why we are doing 12C3 only ?
What about the 4 groups formed of 3 people each ?
In that case will it not be 12C3 + 9C3 + 6C3 + 3C3 ?
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Rumsus
Can anyone explain the answer here ?
Why we are doing 12C3 only ?
What about the 4 groups formed of 3 people each ?
In that case will it not be 12C3 + 9C3 + 6C3 + 3C3 ?

Rumsus

Let's take 4 People and try to make teams of 2.

A B C D
AB
AC
AD
BC
BD
CD

Now try 4C2=6

I tried with 5 people and team of 3 I got the same result as 5C3. You can try that too. Let me know if you are unable to.

So what's happening is the moment you pick 2 people that's a team and we are counting it only once. And that's all that we want.

Hope that helps!
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egmat MartyTargetTestPrep chetan2u VeritasKarishma ScottTargetTestPrep Bunuel
Shouldn't the answer to this question be 12C3*9C3*6C3/4! Since the question states how many "unique teams" can be made?
Curious to know why I'm wrong. Please let me know. Thank you
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Jainam24
egmat MartyTargetTestPrep chetan2u VeritasKarishma ScottTargetTestPrep Bunuel
Shouldn't the answer to this question be 12C3*9C3*6C3/4! Since the question states how many "unique teams" can be made?
Curious to know why I'm wrong. Please let me know. Thank you


The question just asks to make unique teams of 3 persons.

What you are doing is finding different ways in which 12 people can be distributed in 4 teams of 3 person each.

12C3 would mean ABC, DEF, ABD and so on
Your answer means ABC-DEF-GHJ-KLM is one way and then ABD-CEF-GHJ-KLM is another one. Dividing by 4! means the order of the teams does not matter but you will still link 4 different teams to each other and a minor change between two teams will make the way a new one.
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Jainam24
egmat MartyTargetTestPrep chetan2u VeritasKarishma ScottTargetTestPrep Bunuel
Shouldn't the answer to this question be 12C3*9C3*6C3/4! Since the question states how many "unique teams" can be made?
Curious to know why I'm wrong. Please let me know. Thank you

Had the question been "In how many distinct ways can you divide the 12 people into 4 teams of 3 people each?" then your answer would have been correct.
But the question is just asking "How many unique 3 people teams can you make from the 12 people?" so all you need to do is 12C3.
I agree that the question is set up in a way that makes you jump to the solution given by you but that is not what is asked eventually.
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Okay now I got my mistake. Thanks a ton chetan2u and VeritasKarishma
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VeritasKarishma
Jainam24
egmat MartyTargetTestPrep chetan2u VeritasKarishma ScottTargetTestPrep Bunuel
Shouldn't the answer to this question be 12C3*9C3*6C3/4! Since the question states how many "unique teams" can be made?
Curious to know why I'm wrong. Please let me know. Thank you

Had the question been "In how many distinct ways can you divide the 12 people into 4 teams of 3 people each?" then your answer would have been correct.
But the question is just asking "How many unique 3 people teams can you make from the 12 people?" so all you need to do is 12C3.
I agree that the question is set up in a way that makes you jump to the solution given by you but that is not what is asked eventually.


Can you please tell me why we divided by 4! In this case?
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SushantSaini 4! was divided was there because all teams are identical. They aren't different. It is not like team A, B, C and D which makes them distinct.
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From a group of 12 people we can make groups of 3 by using 12C3=220

Ans (C)
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