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Coach Jackson will choose at least two players for his team from those

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Coach Jackson will choose at least two players for his team from those  [#permalink]

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New post Updated on: 15 Dec 2016, 03:03
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Coach Jackson will choose at least two players for his team from those who try out on Saturday. How many players will Coach Jackson choose?

(1) Coach Jackson could choose exactly 20 different teams.
(2) At least two players at the tryout will not be chosen.

Originally posted by Amby02 on 15 Dec 2016, 03:01.
Last edited by Bunuel on 15 Dec 2016, 03:03, edited 1 time in total.
Renamed the topic.
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Coach Jackson will choose at least two players for his team from those  [#permalink]

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New post 15 Dec 2016, 05:43
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Very interesting and, I'd like to say, not an easy question.

Now let's go to our options.

(1) Coach Jackson could choose exactly 20 different teams

That means nCr = 20, where n is our total number of players and r is # of layers we need to choose. The only thing we can actually do is to plug in different values of n and r to get 20 combinations. The most obvious choice is n=20, r=1 and n=20, r = 19. nCr = nCn-r = 20C1=20C19=20. After some time of calculations we’ll find that 6C3 is also equal to 20.

\(6C3 = \frac{6*5*4}{3*2*1} = 20\).

We have three possible values of r = 1, 3, 19.

The phrase "Jackson will choose at least two players" means that 2=< r =< n =< 20. That limits our options to r=3 or r=19. But even two choices means that this option is not sufficient.

(2) At least two players at the tryout will not be chosen.

That means that our r =< n – 2. Said alone without additional data – insufficient.

(1) & (2) taken together: means that our r is in the interval:

2=< r =< 20-2


2 =< r =< 18

And we have only one option left r=3. Sufficient.

Is it really a 600 level question?
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Coach Jackson will choose at least two players for his team from those  [#permalink]

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New post 09 Jan 2017, 12:33
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vitaliyGMAT wrote:
Very interesting and, I'd like to say, not an easy question.

Now let's go to our options.

(1) Coach Jackson could choose exactly 20 different teams

That means nCr = 20, where n is our total number of players and r is # of layers we need to choose. The only thing we can actually do is to plug in different values of n and r to get 20 combinations. The most obvious choice is n=20, r=1 and n=20, r = 19. nCr = nCn-r = 20C1=20C19=20. After some time of calculations we’ll find that 6C3 is also equal to 20.

\(6C3 = \frac{6*5*4}{3*2*1} = 20\).

We have three possible values of r = 1, 3, 19.

The phrase "Jackson will choose at least two players" means that 2=< r =< n =< 20. That limits our options to r=3 or r=19. But even two choices means that this option is not sufficient.

(2) At least two players at the tryout will not be chosen.

That means that our r =< n – 2. Said alone without additional data – insufficient.

(1) & (2) taken together: means that our r is in the interval:

2=< r =< 20-2


2 =< r =< 18

And we have only one option left r=3. Sufficient.

Is it really a 600 level question?



Isn't n= 6 for r=3 ?
Can we use n= 20 while solving for 2<=r<=n-2 ?
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Re: Coach Jackson will choose at least two players for his team from those  [#permalink]

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New post 09 Jan 2017, 13:13
KeepCalmAdi wrote:
vitaliyGMAT wrote:
Very interesting and, I'd like to say, not an easy question.

Now let's go to our options.

(1) Coach Jackson could choose exactly 20 different teams

That means nCr = 20, where n is our total number of players and r is # of layers we need to choose. The only thing we can actually do is to plug in different values of n and r to get 20 combinations. The most obvious choice is n=20, r=1 and n=20, r = 19. nCr = nCn-r = 20C1=20C19=20. After some time of calculations we’ll find that 6C3 is also equal to 20.

\(6C3 = \frac{6*5*4}{3*2*1} = 20\).

We have three possible values of r = 1, 3, 19.

The phrase "Jackson will choose at least two players" means that 2=< r =< n =< 20. That limits our options to r=3 or r=19. But even two choices means that this option is not sufficient.

(2) At least two players at the tryout will not be chosen.

That means that our r =< n – 2. Said alone without additional data – insufficient.

(1) & (2) taken together: means that our r is in the interval:

2=< r =< 20-2


2 =< r =< 18

And we have only one option left r=3. Sufficient.

Is it really a 600 level question?



Isn't n= 6 for r=3 ?
Can we use n= 20 while solving for 2<=r<=n-2 ?


Hi
I can't get the gist of your question.
20 is not the total number of players we need to choose from (n) but the number of combinations of possible team formations. This can be achied when n=20 and n=6.
In 2<=r<=n-2 our max n is 20 and we are discarding second option r=19, because r<=n<=18.
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Re: Coach Jackson will choose at least two players for his team from those  [#permalink]

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New post 09 Jan 2017, 22:26
I realised my mistake.
Thank you.
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Re: Coach Jackson will choose at least two players for his team from those  [#permalink]

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New post 27 May 2018, 21:16
Bunuel
Please help explain the solution for this question.
Question does not mention how many number of players the team consists of.
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Re: Coach Jackson will choose at least two players for his team from those  [#permalink]

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New post 09 Oct 2018, 10:33
Not explained properly....
nCp....n= no of players turned for try out, p= how many coach can choose at a time
therefore- if the coach can form 20 teams......it might mean that nCp= 20. But it is poorly constructed question....This is equivalent to saying that the players can be chosen in 20 ways.....this does not make sense because there is a difference between "20 teams can be formed" and "there are 20 ways to form the team". The question context says the former but conveys the latter....

pl clarify
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Re: Coach Jackson will choose at least two players for his team from those   [#permalink] 09 Oct 2018, 10:33
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Coach Jackson will choose at least two players for his team from those

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