Last visit was: 20 Jun 2024, 02:49 It is currently 20 Jun 2024, 02:49
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 93832
Own Kudos [?]: 633256 [20]
Given Kudos: 82387
Send PM
Senior Manager
Senior Manager
Joined: 24 Apr 2016
Posts: 255
Own Kudos [?]: 693 [4]
Given Kudos: 48
Send PM
Manager
Manager
Joined: 30 May 2017
Posts: 57
Own Kudos [?]: 62 [0]
Given Kudos: 42
Concentration: Finance, General Management
GMAT 1: 690 Q47 V38
GPA: 3.23
Send PM
Manager
Manager
Joined: 24 Dec 2016
Posts: 62
Own Kudos [?]: 195 [2]
Given Kudos: 153
Location: Armenia
Concentration: Statistics
GMAT 1: 720 Q49 V40
GMAT 2: 770 Q50 V47
GPA: 3.4
WE:Consulting (Consulting)
Send PM
Re: An engagement team consists of a project manager, team leader, and [#permalink]
2
Kudos
C
The number of ways to choose the project manager is 2 and the number of ways to choose a team leader is 3.
The total number of ways to choose 4 consultants out of 7 candidates is 7!/(4!3)= 35, however, we must also take into the consideration that 2 candidates refuse to work together and for that reason, we must deduct from the total number of ways all the options when these 2 are together. We do it by counting all the outcomes, when these 2 are already in team and there are still 2 spots available: 5!/(2!*3!) = 10, so there are 35-10=25 ways of picking 4 candidates out of 7, taking into the consideration the fact that 2 of them don't want to work together. The only thing that remains now is to multiply all outcomes 2*3*25=150
Manager
Manager
Joined: 02 Feb 2016
Posts: 75
Own Kudos [?]: 45 [0]
Given Kudos: 40
GMAT 1: 690 Q43 V41
Send PM
Re: An engagement team consists of a project manager, team leader, and [#permalink]
quantumliner wrote:
Project manager - 2
Team leader - 3
Four consultants - 7

Total number of combinations = 2\(C_1\) * 3\(C_1\) * 7\(C_4\) = 2*3*35 = 210


Total number of combinations when both consultants are together = 2\(C_1\) * 3\(C_1\) * 5\(C_2\) = 2*3*10=60

Number of Teams possible = 210-60 = 150

Answer is C


How do we get 5C2 when we calculate the total number of combinations when consultants are together?
Board of Directors
Joined: 18 Jul 2015
Status:Emory Goizueta Alum
Posts: 3598
Own Kudos [?]: 5449 [4]
Given Kudos: 346
Send PM
Re: An engagement team consists of a project manager, team leader, and [#permalink]
2
Kudos
2
Bookmarks
Expert Reply
TheMastermind wrote:
How do we get 5C2 when we calculate the total number of combinations when consultants are together?


Hi TheMastermind ,

When I am saying two consultants are always together, that means I already have them on my bucket and now I have to select the pending 2 from the remaining 5 consultants. Thus, we are using 5C2

Let me know if you need the detailed explanation for this question. :)
Manager
Manager
Joined: 14 Feb 2014
Posts: 92
Own Kudos [?]: 19 [0]
Given Kudos: 4003
Send PM
An engagement team consists of a project manager, team leader, and [#permalink]
abhimahna Bunuel

I understand the first approach: 2C1 * 3C1 * 7C4 = 2*3*35 = 210

What i donot understand is: Total number of combinations when both consultants are together = 2C1 * 3C1 * 5C2 = 2*3*10=60

I have no idea where the 5C2 comes from instead i have 6C2. If we want to calculate the number of combination that the two consultant are together, we use the Glue methode by compressing the 2 into 1 + the other remaing 5. then we get 6. Then we perform 6C2.

In the end i get this: 210 - (2)(3)(6C2)2!= 210 - (2)(3)(30) = 210 - 180 = 30


Where do i go wrong and where does the 5C2 come from?



Thanks in advance!­
Intern
Intern
Joined: 29 Apr 2022
Posts: 6
Own Kudos [?]: 1 [0]
Given Kudos: 2
Send PM
Re: An engagement team consists of a project manager, team leader, and [#permalink]
­Select 1 out of 2 PM
Select 1 out of 3 TL
For Consultants there are 7 and 4 to be selected and 2 cant remain in 1 team

Case 1 : One is chosen then total consultant choices 5C3
Case 2: Other is chosen then total consultant choices 5C3
Case 3: None are chosen then total consultant choices 5C4 (both are not selected)

so total choice of consultants = 5C3 + 5C3 + 5C4

Overall choice one after the other = 2C1 X 3C1 X (5C3 + 5C3 + 5C4) = 150 
GMAT Club Bot
Re: An engagement team consists of a project manager, team leader, and [#permalink]
Moderator:
Math Expert
93832 posts