November 17, 2018 November 17, 2018 07:00 AM PST 09:00 AM PST Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. November 17, 2018 November 17, 2018 09:00 AM PST 11:00 AM PST Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.
Author 
Message 
TAGS:

Hide Tags

Current Student
Joined: 19 Mar 2012
Posts: 4426
Location: India
GPA: 3.8
WE: Marketing (NonProfit and Government)

A teacher wants to select a team of 5 players from a group
[#permalink]
Show Tags
19 Apr 2018, 03:26
Question Stats:
64% (02:11) correct 36% (01:46) wrong based on 244 sessions
HideShow timer Statistics




PS Forum Moderator
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 370

Re: A teacher wants to select a team of 5 players from a group
[#permalink]
Show Tags
19 Apr 2018, 04:01
souvik101990 wrote: 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 Based on the constraints there could be two types of teams: 1. One with both Jane and Sue. 2. One without either. 1. # Of ways to select team with both Jane and Sue. = 7C3 ( Select the other three team members as Jane and Sue are a given) = 35. 2. # of ways to select a team without Jane and Sue. = 7C5 = 21. Total numbers of teams possible is 1. + 2. Hence # teams = 35 + 21 = 56. Hence Option (C) is our answer. Best, Gladi




Intern
Joined: 03 Aug 2016
Posts: 40

Re: A teacher wants to select a team of 5 players from a group
[#permalink]
Show Tags
Updated on: 19 Apr 2018, 04:08
souvik101990 wrote: 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 Without any restriction we can select 5 players from a team of 9 by > 9C5 = 9!/(4!5!) = 126 ways. Restriction: If Jane is in the team, Sue should also be in the team. So we'll treat Jane and Sue as one group, and between them they can arrange in 2! ways = 2 ways. Now, we need to select 3 more players out of 7 (as Jane and Sue are already in the team), which can be done by 7C3 = 7!/(4!*3!) = 35 ways. Total = 35*2 = 70 ways Total > 126  70 = 56 ways.
_________________
Please press +1 Kudos if you find my post/reply helpful
Originally posted by Wildflower on 19 Apr 2018, 03:59.
Last edited by Wildflower on 19 Apr 2018, 04:08, edited 1 time in total.



Manager
Joined: 30 May 2017
Posts: 122
Location: United States
GPA: 3.57

Re: A teacher wants to select a team of 5 players from a group
[#permalink]
Show Tags
19 Apr 2018, 04:02
souvik101990 wrote: 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 There are 2 ways to arrange the team First option. Jane and Sue are selected in the team. Therefore we have to choose 3 additional team members from 7 = (9(Jane+Sue)) = 92 7!/(4!3!) = 7*6*5/3! = 35 Second option. Jane and Sue are outside the team. Therefore we have to choose 5 team members from 7 = (9(Jane+Sue)) = 92 7!/(5!2!) = 7*6/2! = 21 Our answer is addition of two options above 35+21 = 56. Hence option C = 56 is the answer.
_________________
Kindly press the +1Kudos if you like the explanation. Thanks a lot!!!



Intern
Joined: 26 Jan 2018
Posts: 11
Location: India
Concentration: Finance, International Business
GPA: 4
WE: Human Resources (Computer Software)

Re: A teacher wants to select a team of 5 players from a group
[#permalink]
Show Tags
19 Apr 2018, 04:39
Gladiator59 has already provided the method I thought of, so I am late to this party! Wildflower thank you for sharing a different perspective!



Intern
Joined: 03 Aug 2016
Posts: 40

Re: A teacher wants to select a team of 5 players from a group
[#permalink]
Show Tags
19 Apr 2018, 04:45
tll001 wrote: Gladiator59 has already provided the method I thought of, so I am late to this party! Wildflower thank you for sharing a different perspective! You're welcome! This is my usual approach
_________________
Please press +1 Kudos if you find my post/reply helpful



Manager
Joined: 03 Oct 2016
Posts: 128

Re: A teacher wants to select a team of 5 players from a group
[#permalink]
Show Tags
19 Apr 2018, 05:02
souvik101990 wrote: 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 \(7C5\) > Picking 5 players (excluding Jane & Sue) out of remaining 7 players to form the team. \(7C3\)> Picking 3 players (considering Jane & Sue are already there in the team) out of 7 remaining players to form the team. \(7C5\)+\(7C3\)=21+35=56 (C).
_________________
NonAllergic To Kudos



Intern
Joined: 08 Jan 2018
Posts: 3

Re: A teacher wants to select a team of 5 players from a group
[#permalink]
Show Tags
19 Apr 2018, 05:10
Selecting 5 players from a group of 9 players: Selected  Not selected _ _ _ _ _  _ _ _ _
1. Given that there is no constraints, there are 9C5 = \frac{9!}{(5!*(94)!)} = 126 ways to arrange.
2. Given that Jane and Sue has to be on the same team, calculate number of ways given if Sue is in the team, Jane is not in the team or vise versa.
_ _ _ _ J  _ _ _ S or _ _ _ _ S  _ _ _ J
Ignoring J and S as they are fixed, there are 2*(7C4) = \frac{7!}{(4!*(74)!)} = 70 ways. _ _ _ _  _ _ _
Subtracting 2 from 1, 126 Ways  70 Ways = 56 Ways.
The answer is C) 56



Intern
Joined: 19 Apr 2018
Posts: 7

Re: A teacher wants to select a team of 5 players from a group
[#permalink]
Show Tags
19 Apr 2018, 05:52
Hello, dear friends! to be honest, I am not sure, but i think that the correct answer is E. Is it so or not?



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2201

Re: A teacher wants to select a team of 5 players from a group
[#permalink]
Show Tags
19 Apr 2018, 21:24



Intern
Joined: 08 Aug 2013
Posts: 14
Location: India
GPA: 4

Re: A teacher wants to select a team of 5 players from a group
[#permalink]
Show Tags
21 Apr 2018, 07:44
souvik101990 wrote: 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 Ans: C Case 1: Either of Jane and Sue is selected. In this case , both will be part of the team. Therefore, remaining 3 person can be selected from remaining 7 of the players in 7c3 ways. ie. 35 ways. Case 2: Neither of 2 is elected. So, 5 player can be selected from remaining 7 people in 7c5 ways. i.e. 21 ways Therefore, total ways: case1+ case 2= 35+21=56



Intern
Joined: 10 May 2016
Posts: 18
Location: India
GPA: 3.9

Re: A teacher wants to select a team of 5 players from a group
[#permalink]
Show Tags
21 Apr 2018, 13:28
souvik101990 wrote: 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 The correct answer is option C. Here is why:This is a Permutation & Combination question, which can be solved easily if the basic concepts are clear. In the question Jane and Sue need to be included in a team. So either 1) they are selected or 2) they aren't selected  no cases where only one of them is selected. Important to note, there is no importance of who is selected first. The number of ways will be the sum of both the ways both cases are selected  1) Since the two are already selected, 3 teammates need to be selected from the remaining 7 i.e. 7C3 =35 2) In this case, the two can't be selected. So all 5 need to be selected from the remaining 7 i.e. 7C5 =21 Total = 35 +21 =56 Hence Option C



Intern
Joined: 09 Jun 2012
Posts: 27
Location: India

Re: A teacher wants to select a team of 5 players from a group
[#permalink]
Show Tags
21 Apr 2018, 22:22
souvik101990 wrote: 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 there will be two cases: 1. Jane and sue are in the team 2. Jane and sue are not in the team Case 1. 3 players need to be selected from remaining 7 = 7C3 =35 Case 2. 5 players need to be selected from remaining 7= 7C5= 21 so, total no. of ways = 35+21= 56 Correct Answer= C
_________________
Please press +1 Kudos if you find my post/reply helpful



Current Student
Joined: 19 Mar 2012
Posts: 4426
Location: India
GPA: 3.8
WE: Marketing (NonProfit and Government)

Re: A teacher wants to select a team of 5 players from a group
[#permalink]
Show Tags
23 Apr 2018, 06:57



Intern
Joined: 03 Aug 2016
Posts: 40

Re: A teacher wants to select a team of 5 players from a group
[#permalink]
Show Tags
23 Apr 2018, 08:28
souvik101990 wrote: Wildflower  GREAT job on this one! PM me to get your GMAT Club tests! Yay! Thank you!
_________________
Please press +1 Kudos if you find my post/reply helpful



Intern
Joined: 28 Sep 2017
Posts: 8

Re: A teacher wants to select a team of 5 players from a group
[#permalink]
Show Tags
26 Apr 2018, 03:31
Because Jane and Sue have to be chosen simultaneously. So, there are 2 scenarios: they are chosen and they are not
If they are chosen, there are left with 3 choices in 7 people > we have 7C3 = 35 ways to form a suitable team. If they are not chosen, there are left with 5 choices in 7 people > we have 7C5 = 21 ways
Combine 2 scenarios > 35+ 21 = 56 > C



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2201

A teacher wants to select a team of 5 players from a group
[#permalink]
Show Tags
27 Apr 2018, 04:28
Solution Given:• A group contain 9 players. • Jane and Sue are 2 such players in the group. To find: • The number of ways in which the teacher can select a team of 5 players from the 9 players in the group. Approach and Working out: • The only constraint given in the question is that the team either consists both Jane and Sue, or, consist none of them. o Thus, it is better to solve the sum keeping the two conditions in mind. Case 1: When both Jane and Sue are in the team. In this case, two out of the five players are already in the team. Thus, we need to select 3 more players. The total number of players from which we can select 3 = 9 2(Jane and Sue) = 7 Ways to select 3 players from 7 players = \(^7c_3\). Case 2: When neither Jane nor Sue is in the team. In this case, we need to select 5 players from 7 players. (Because we cannot consider Jane and Sue in the team) Ways to select 5 players from 7 players = \(^7c_5\) Since both the above cases can be true, we will add them to get the final answer. Ways to choose the team = \(^7c_3\) + \(^7c_5\) = 56 Hence, the correct answer is option C.
_________________
Register for free sessions Number Properties  Algebra Quant Workshop
Success Stories Guillermo's Success Story  Carrie's Success Story
Ace GMAT quant Articles and Question to reach Q51  Question of the week
Must Read Articles Number Properties – Even Odd  LCM GCD  Statistics1  Statistics2 Word Problems – Percentage 1  Percentage 2  Time and Work 1  Time and Work 2  Time, Speed and Distance 1  Time, Speed and Distance 2 Advanced Topics Permutation and Combination 1  Permutation and Combination 2  Permutation and Combination 3  Probability Geometry Triangles 1  Triangles 2  Triangles 3  Common Mistakes in Geometry Algebra Wavy line  Inequalities Practice Questions Number Properties 1  Number Properties 2  Algebra 1  Geometry  Prime Numbers  Absolute value equations  Sets
 '4 out of Top 5' Instructors on gmatclub  70 point improvement guarantee  www.egmat.com



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2201

Re: A teacher wants to select a team of 5 players from a group
[#permalink]
Show Tags
27 Apr 2018, 04:38
Alternate Solution Given: • A group contain 9 players. • Jane and Sue are 2 such players in the group. To find: • The number of ways in which the teacher can select a team of 5 players from the 9 players in the group. Approach and Working out: • If either one of Jane or Sue is in the team, our given condition will be void. o If we subtract these cases from the total possible cases, we will reach the answer. • Thus, we can write: o Total Possible selections = Total selections (Without Constraint) – Total selections where either Jane or Sue, but not both is in the team. Note: When we are selecting either Jane or Sue, we must select 4 players from the remaining 7 players (9 – Jane and Sue) and 1 from Jane and Sue. Total Selections (Without Constraints) = \(^9c_5\) = 126. Total selections where either Jane or Sue, but not both is in the team = \(^7c_4\) * \(^2c_1\) = 70 Total required selections = 126 – 70 = 56. Hence, the correct answer is option C.
_________________
Register for free sessions Number Properties  Algebra Quant Workshop
Success Stories Guillermo's Success Story  Carrie's Success Story
Ace GMAT quant Articles and Question to reach Q51  Question of the week
Must Read Articles Number Properties – Even Odd  LCM GCD  Statistics1  Statistics2 Word Problems – Percentage 1  Percentage 2  Time and Work 1  Time and Work 2  Time, Speed and Distance 1  Time, Speed and Distance 2 Advanced Topics Permutation and Combination 1  Permutation and Combination 2  Permutation and Combination 3  Probability Geometry Triangles 1  Triangles 2  Triangles 3  Common Mistakes in Geometry Algebra Wavy line  Inequalities Practice Questions Number Properties 1  Number Properties 2  Algebra 1  Geometry  Prime Numbers  Absolute value equations  Sets
 '4 out of Top 5' Instructors on gmatclub  70 point improvement guarantee  www.egmat.com



Director
Joined: 02 Oct 2017
Posts: 694

Re: A teacher wants to select a team of 5 players from a group
[#permalink]
Show Tags
06 May 2018, 08:01
5 team player need to be selected from 9 players I) when Jane and Sue selected then 3 players need to be selected from 7 So 7C3=35 II)none from Jane and Sue selected 5 need to be selected from 7 So 7C5=21 Total= 35+21=56 Posted from my mobile device
_________________
Give kudos if you like the post



Director
Joined: 27 May 2012
Posts: 606

Re: A teacher wants to select a team of 5 players from a group
[#permalink]
Show Tags
11 Sep 2018, 06:07
souvik101990 wrote: 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 Dear Moderator, Please untag probability, Thank you.
_________________
 Stne




Re: A teacher wants to select a team of 5 players from a group &nbs
[#permalink]
11 Sep 2018, 06:07



Go to page
1 2
Next
[ 24 posts ]



