BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

In a row of 30 seats, six-team of 4 persons each will be seated. The members of any one team always sit...

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 2505
Joined: Sun Oct 15, 2017 1:50 pm
Followed by:6 members

In a row of 30 seats, six-team of 4 persons each will be seated. The members of any one team always sit...

by BTGmoderatorLU » Tue May 26, 2020 6:27 am
Source: Magoosh

In a row of 30 seats, six-team of 4 persons each will be seated. The members of any one team always sit together in four consecutive seats in the same order. Different teams may be adjacent or separated by empty seats. In how many ways can the six teams be seated in the 30 seats?

A. (6!)(6!)
B. (12!)/(6!)
C. 12C6
D. 30C12
E. 30C6*6

The OA is B
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

Re: In a row of 30 seats, six-team of 4 persons each will be seated. The members of any one team always sit...

by Jay@ManhattanReview » Wed May 27, 2020 1:09 am
BTGmoderatorLU wrote: ↑
Tue May 26, 2020 6:27 am
 Source: Magoosh

In a row of 30 seats, six-team of 4 persons each will be seated. The members of any one team always sit together in four consecutive seats in the same order. Different teams may be adjacent or separated by empty seats. In how many ways can the six teams be seated in the 30 seats?

A. (6!)(6!)
B. (12!)/(6!)
C. 12C6
D. 30C12
E. 30C6*6

The OA is B
Since all members of a team are to sit together, let's club 4 members of each team. Say the teams are T1, T2, T3, T4, T5, and T6. So, we have 30 – 6*4 = 6 empty seats and 6-sets of the occupied seat, with each set has 4 seats.

So, the situation is T1, T2, T3, T4, T5, T6, E, E, E, E, E, E; where E = empty seat

So, the no. of ways 12 sets can be occupied out of 12 sets = 12!/6!; I divided 12! by 6! since 6 Es are identical.

The correct answer: B

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: Manhattan Review Warangal | Hyderabad | GRE Prep Mumbai | Visakhapatnam GRE Coaching | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8085
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

Re: In a row of 30 seats, six-team of 4 persons each will be seated. The members of any one team always sit...

by Scott@TargetTestPrep » Sat May 30, 2020 1:38 pm
BTGmoderatorLU wrote: ↑
Tue May 26, 2020 6:27 am
 Source: Magoosh

In a row of 30 seats, six-team of 4 persons each will be seated. The members of any one team always sit together in four consecutive seats in the same order. Different teams may be adjacent or separated by empty seats. In how many ways can the six teams be seated in the 30 seats?

A. (6!)(6!)
B. (12!)/(6!)
C. 12C6
D. 30C12
E. 30C6*6

The OA is B
Solution:

We can let the 6 teams be A, B, C, D, E and F and let S be an empty seat. Since there must be 6 empty seats, therefore, one seating arrangement is ABCDEFSSSSSS. Now we need to determine the number of ways we can arrange these 12 “letters.” By the formula for the permutation of indistinguishable objects, we see that these 12 “letters” can be arranged in 12! / 6! ways.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1