GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 04 Aug 2020, 23:59

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

PS- Permutation & Combination Question

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Intern
Intern
avatar
B
Joined: 08 May 2020
Posts: 4
PS- Permutation & Combination Question  [#permalink]

Show Tags

New post 14 Jul 2020, 13:48
2
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

60% (03:04) correct 40% (01:36) wrong based on 10 sessions

HideShow timer Statistics

A school has vacancy for a librarian, a Physics teacher, and four Computer teachers. There are 3 candidates for the position of Librarian, 2 candidates for the position of Physics teacher, and 7 candidates for the position of computer teachers. If 2 out of 7 computer teachers refuse to be on the same team, how many different ways are there to fill the vacancies are possible?


    35
    150
    210
    60
    70
GMAT Tutor
User avatar
S
Joined: 16 Sep 2014
Posts: 559
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
PS- Permutation & Combination Question  [#permalink]

Show Tags

New post 14 Jul 2020, 15:24
1
Kav24 wrote:
A school has vacancy for a librarian, a Physics teacher, and four Computer teachers. There are 3 candidates for the position of Librarian, 2 candidates for the position of Physics teacher, and 7 candidates for the position of computer teachers. If 2 out of 7 computer teachers refuse to be on the same team, how many different ways are there to fill the vacancies are possible?


    35
    150
    210
    60
    70



For the librarian there are 3 options, for the physics teacher there are 2 options. The key part is the number of viable arrangement for 4 computer teachers.

Typically we would find 7C4 = 7C3 = 7 * 6 * 5 / (3!) = 35 combinations, yet there are 2 teachers that do not want to be in the same group. We may count how many groups have those 2 teachers and subtract that number from 35 to find the number of desired groups for computer teachers.

We need to form a group of 4, two spots are filled in with the two teachers mentioned above, and the other 2 spots must be filled in from the rest of the 5 computer teachers. Therefore there are 5C2 groups out of the 7C4 groups we cannot take.

Out of the 7C4 = 35 combinations, we must remove 5C2 = 5 * 4 / 2! = 10 options that represent the case where these two teachers are grouped. Therefore 35 - 10 = 25 groups are available for computer teachers.

Finally 3 * 2 * 25 = 150 would be the answer.

Ans: B
_________________
Source: We are an NYC based, in-person and online GMAT tutoring and prep company. We are the only GMAT provider in the world to guarantee specific GMAT scores with our flat-fee tutoring packages, or to publish student score increase rates. Our typical new-to-GMAT student score increase rate is 3-9 points per tutoring hour, the fastest in the world. Feel free to reach out!
Manager
Manager
User avatar
S
Status: BELIEVE IN YOURSELF
Joined: 06 Oct 2019
Posts: 98
Location: India
Re: PS- Permutation & Combination Question  [#permalink]

Show Tags

New post 14 Jul 2020, 17:50
1
Kav24 wrote:
A school has vacancy for a librarian, a Physics teacher, and four Computer teachers. There are 3 candidates for the position of Librarian, 2 candidates for the position of Physics teacher, and 7 candidates for the position of computer teachers. If 2 out of 7 computer teachers refuse to be on the same team, how many different ways are there to fill the vacancies are possible?


    35
    150
    210
    60
    70


Ways to select librarian =3C1
Ways to select physics teacher =2C1
Ways to select computer teacher=7C4

But, as the question mentioned 2 out of those 7 candidates for position of computer teacher are refuse to be on the same team

Lets calculate the number of ways if the 2 candidates want always to be on the same team

Let the 7 candidate be
A,B,C,D,E,F,G

And among those let A,B decided to be on same team

Team of 4 two already filled A,B rest 2 spot fill by 5C2 ways


3C1*2C1*(7C4-5C2)=150 ways

Posted from my mobile device
GMAT Club Bot
Re: PS- Permutation & Combination Question   [#permalink] 14 Jul 2020, 17:50

PS- Permutation & Combination Question

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne