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# A teacher wants to select a team of 5 players from a group

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Joined: 02 Sep 2009
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Re: A teacher wants to select a team of 5 players from a group  [#permalink]

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11 Sep 2018, 07:29
stne wrote:
souvik101990 wrote:

GST Week 2 Day 3 e-GMAT Question 3

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A teacher wants to select a team of 5 players from a group of 9 players. However, she needs to keep the following constraints in mind: If Jane is in the team, Sue should also be included in the team and vice versa.

In how many ways can the teacher select the team for a tournament?:

A) 21
B) 35
C) 56
D) 120
E) 126

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Re: A teacher wants to select a team of 5 players from a group  [#permalink]

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14 Sep 2018, 17:48
souvik101990 wrote:

GST Week 2 Day 3 e-GMAT Question 3

Give your best shot at writing a top notch application and you will have the chance to win GMAT Club tests daily and e-GMAT Quant Online Course . See the GMAT Spring Training Thread for all details

A teacher wants to select a team of 5 players from a group of 9 players. However, she needs to keep the following constraints in mind: If Jane is in the team, Sue should also be included in the team and vice versa.

In how many ways can the teacher select the team for a tournament?:

A) 21
B) 35
C) 56
D) 120
E) 126

If both Sue and Jane do make the team, the number of ways to select the team is 7C3 since we need to select 3 more players from the remaining 7 players:

7C3 = 7!/(3! x 4!) = (7 x 6 x 5)/3! = 35 ways

If both Sue and Jane do not make the team, the number of ways to select the team is 7C5:

7C5 = (7 x 6 x 5 x 4 x 3)/(5 x 4 x 3 x 2) = 7 x 3 = 21 ways

So the total possible ways is 35 + 21 = 56.

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Re: A teacher wants to select a team of 5 players from a group  [#permalink]

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31 Oct 2018, 00:33
If Jane is in the team, Sue should also be included in the team and VICE VERSA.
VICE VERSA could be interpreted as : If Sue is in the team, Jane should also be included in the team.
Isn't this question a little bit ambiguous?
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Re: A teacher wants to select a team of 5 players from a group  [#permalink]

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31 Oct 2018, 00:46
abdugafur wrote:
If Jane is in the team, Sue should also be included in the team and VICE VERSA.
VICE VERSA could be interpreted as : If Sue is in the team, Jane should also be included in the team.
Isn't this question a little bit ambiguous?

abdugafur I won't call it an ambiguous question however it would have been better to state that 'Sue and Jane must be chosen together in team as they can't work in absence of each other'
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Re: A teacher wants to select a team of 5 players from a group  [#permalink]

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16 Feb 2019, 23:35
souvik101990 wrote:

GST Week 2 Day 3 e-GMAT Question 3

Give your best shot at writing a top notch application and you will have the chance to win GMAT Club tests daily and e-GMAT Quant Online Course . See the GMAT Spring Training Thread for all details

A teacher wants to select a team of 5 players from a group of 9 players. However, she needs to keep the following constraints in mind: If Jane is in the team, Sue should also be included in the team and vice versa.

In how many ways can the teacher select the team for a tournament?:

A) 21
B) 35
C) 56
D) 120
E) 126

Total ways without any restriction => $$9C_5$$ = 126 ways

Now we put restriction(where either one is in team) then it will be = $$2* 7C_4$$= 70 ways

Now we can calculate If Jane is in the team, Sue should also be included in the team and vice versa.
= 126 - 70
= 56 ways

C
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Re: A teacher wants to select a team of 5 players from a group  [#permalink]

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11 Apr 2019, 11:10
Hi All,

We're told that a teacher wants to select a team of 5 players from a group of 9 players. However, she needs to keep the following constraints in mind: If Jane is in the team, Sue should also be included in the team and vice versa. We're asked for the number of different ways that the teacher can select the team for a tournament. This question is a Combination Formula question with a 'twist': you either need BOTH girls on the team OR you need NEITHER girl on the team. Those two options require slightly different calculations.

Combination Formula = N!/K!(N-K)! where N is the total number of people and K is the size of the subgroup.

For Jane and Sue to be on the team, those two players would take 2 of the 5 'spots', so the other 3 spots would be chosen from the remaining 7 players...
7!/3!(7-3)! = (7)(6)(5)/(3)(2)(1) = 35 options

For NEITHER Jane NOR Sue to be on the team, the 5 'spots' would be chosen from the other 7 players...
7!/5!(7-5)! = (7)(6)/(2)(1) = 21 options

Total possible teams = 35 + 21 = 56

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Re: A teacher wants to select a team of 5 players from a group   [#permalink] 11 Apr 2019, 11:10

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