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In a row of 30 seats, six team of 4 persons each will be seated. The

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Magoosh GMAT Instructor
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In a row of 30 seats, six team of 4 persons each will be seated. The  [#permalink]

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New post 15 Sep 2016, 15:11
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Question Stats:

35% (02:11) correct 65% (02:06) wrong based on 81 sessions

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This question was inspired by another current question that appears to be less than fully clear:
there-is-a-row-of-30-seats-and-there-are-6-groups-of-4-persons-each-225526.html

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) \(\frac{12!}{6!}\)

(C) 12C6

(D) 30C12

(E) 30C6*6

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Mike McGarry
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Re: In a row of 30 seats, six team of 4 persons each will be seated. The  [#permalink]

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New post 15 Sep 2016, 17:27
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1
mikemcgarry wrote:
This question was inspired by another current question that appears to be less than fully clear:
there-is-a-row-of-30-seats-and-there-are-6-groups-of-4-persons-each-225526.html

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) \(\frac{12!}{6!}\)

(C) 12C6

(D) 30C12

(E) 30C6*6



Hi,
There are total 30 seats, but 4 members of 6 different groups always sit together and in same sequence...
So the group can be taken as one seat, making the total as 12 seats..

12 seats include 6 empty chairs as total 6*4 chairs are filled in 30 seats and these 6 seats will be identical while the other 6 would be different as each consists of different group..
Ans 12!/6!
B
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: In a row of 30 seats, six team of 4 persons each will be seated. The  [#permalink]

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New post 17 Sep 2016, 07:58
Hi Chetan,

Im unable to undertand your explaination. Because the teams will have the same arrangement, we will have essentially 24/4 i.e 6 places+the remaining empty seats i.e 6; so the total becomes 12!. 12! is the answer according to me, please explain what is wrong.

thanks,
Jon
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Re: In a row of 30 seats, six team of 4 persons each will be seated. The  [#permalink]

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New post 17 Sep 2016, 08:39
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TheLordCommander wrote:
Hi Chetan,

Im unable to undertand your explaination. Because the teams will have the same arrangement, we will have essentially 24/4 i.e 6 places+the remaining empty seats i.e 6; so the total becomes 12!. 12! is the answer according to me, please explain what is wrong.

thanks,
Jon


Hi Jon,

You are correct till 12! ...
But the 6 empty seats are same and this 6 seats can be arranged in 6! Ways ...
That is why we divide 12! By 6!
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: In a row of 30 seats, six team of 4 persons each will be seated. The  [#permalink]

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New post 22 Dec 2018, 00:06
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say,team 1 =T1 and team2 =T2
like this we have T3,T4,T5,T6
EACH TEAM CONSISTS OF 4 MEMBERS, SO 6 SEATS ARE REMAINING EMPTY.
and each empty seat = E

ultimately question becomes in how many different way you can arrange T1,T2,T3,T4,T5,T6,E,E,E,E,E,E

= \(12!/6!\)

note- you do not need to multiple by 4! to arrange members of each team as question has clearly stated.
Quote:
The members of any one team always sit together in four consecutive seats in the same order.

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Re: In a row of 30 seats, six team of 4 persons each will be seated. The &nbs [#permalink] 22 Dec 2018, 00:06
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