It is currently 12 Dec 2017, 15:52

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# An engagement team consists of a project manager, team leader, and

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 42571

Kudos [?]: 135392 [0], given: 12691

An engagement team consists of a project manager, team leader, and [#permalink]

### Show Tags

06 Jun 2017, 10:32
Expert's post
7
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

71% (02:09) correct 29% (02:18) wrong based on 115 sessions

### HideShow timer Statistics

An engagement team consists of a project manager, team leader, and four consultants. There are 2 candidates for the position of project manager, 3 candidates for the position of team leader, and 7 candidates for the 4 consultant slots. If 2 of the 7 consultants refuse to be on the same team, how many different teams are possible?

A. 25
B. 35
C. 150
D. 210
E. 300
[Reveal] Spoiler: OA

_________________

Kudos [?]: 135392 [0], given: 12691

Senior Manager
Joined: 24 Apr 2016
Posts: 334

Kudos [?]: 196 [0], given: 48

An engagement team consists of a project manager, team leader, and [#permalink]

### Show Tags

06 Jun 2017, 11:34
Project manager - 2
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

Last edited by quantumliner on 13 Jun 2017, 15:09, edited 1 time in total.

Kudos [?]: 196 [0], given: 48

Manager
Joined: 30 May 2017
Posts: 55

Kudos [?]: 20 [0], given: 37

Concentration: Finance, General Management
GMAT 1: 690 Q47 V38
GPA: 3.25
Re: An engagement team consists of a project manager, team leader, and [#permalink]

### Show Tags

13 Jun 2017, 13:58
Quote:
Total number of combinations when both consultants are together

Should total up to 60 vice 40.
_________________

Veritas Prep 6/18/17 600 Q:38 V:35 IR:5
Veritas Prep 6/29/17 620 Q:43 V:33 IR:4
Manhattan 7/12/17 640 Q:42 V:35 IR:2.4
Veritas Prep 7/27/17 640 Q:41 V:37 IR:4
Manhattan 8/9/17 670 Q:44 V:37 IR:3
Veritas Prep 8/21/17 660 Q:45 V:36 IR:7
GMAT Prep 8/23/17 700 Q:47 V:38 IR:8
GMAT Prep 8/27/17 730 Q:49 V:40 IR:8
Veritas Prep 8/30/17 690 Q:47 V:37 IR:8

Kudos [?]: 20 [0], given: 37

Manager
Joined: 23 Dec 2016
Posts: 65

Kudos [?]: 40 [1], given: 41

Schools: Fuqua
GMAT 1: 720 Q49 V40
GPA: 3.21
Re: An engagement team consists of a project manager, team leader, and [#permalink]

### Show Tags

13 Jun 2017, 15:48
1
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
_________________

If you find my solution useful, hit the "Kudos" button

Kudos [?]: 40 [1], given: 41

Manager
Joined: 02 Feb 2016
Posts: 90

Kudos [?]: 9 [0], given: 40

GMAT 1: 690 Q43 V41
Re: An engagement team consists of a project manager, team leader, and [#permalink]

### Show Tags

02 Aug 2017, 12:25
quantumliner wrote:
Project manager - 2
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

How do we get 5C2 when we calculate the total number of combinations when consultants are together?

Kudos [?]: 9 [0], given: 40

Board of Directors
Status: Aiming MBA
Joined: 18 Jul 2015
Posts: 2857

Kudos [?]: 965 [0], given: 69

Location: India
Concentration: Healthcare, Technology
GPA: 3.65
WE: Information Technology (Health Care)
Re: An engagement team consists of a project manager, team leader, and [#permalink]

### Show Tags

03 Aug 2017, 05:08
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.
_________________

How I improved from V21 to V40! ?

Kudos [?]: 965 [0], given: 69

Re: An engagement team consists of a project manager, team leader, and   [#permalink] 03 Aug 2017, 05:08
Display posts from previous: Sort by