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A group of 8 students take up a full row at a movie theater 04 Sep 2013, 14:37
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C
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79% (01:41) correct 21% (02:36) wrong based on 529 sessions

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A group of 8 students take up a full row at a movie theater. There are 2 couples and the 2 people within each couple must sit together. in how many arrangements can the students sit?

A.1296
B.1850
C.2880
D.3546
E.4200
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C
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A group of 8 students take up a full row at a movie theater 04 Sep 2013, 14:59
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bagdbmba
A group of 8 students take up a full row at a movie theater. There are 2 couples and the 2 people within each couple must sit together. in how many arrangements can the students sit?

A.1296
B.1850
C.2880
D.3546
E.4200
Show more

Glue couples together: {AB}, {CD}.

6 units {AB}, {CD}, {E}, {F}, {G}, {H} can be arranged in 6! ways. Each couple within their unit can be arranged in 2! ways.

Therefore the final answer is 6!*2!*2!=2,880.

Answer: C.
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A group of 8 students take up a full row at a movie theater 04 Sep 2013, 20:03
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A group of 8 students take up a full row at a movie theater. There are 2 couples and the 2 people within each couple must sit together. in how many arrangements can the students sit?

A.1296
B.1850
C.2880
D.3546
E.4200

Glue couples together: {AB}, {CD}.

6 units {AB}, {CD}, {E}, {F}, {G}, {H} can be arranged in 6! ways. Each couple within their unit can be arranged in 2! ways.

Therefore the final answer is 6!*2!*2!=2,880.

Answer: C.
Show more

Bunuel,
Thanks for your explanation but I'm getting confused with this part "There are 2 couples and the 2 people within each couple must sit together" particularly...

As we do 6!, how then can two people within each couple must sit together as per the above statement?

Please help!
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A group of 8 students take up a full row at a movie theater 04 Sep 2013, 20:30
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bagdbmba
A group of 8 students take up a full row at a movie theater. There are 2 couples and the 2 people within each couple must sit together. in how many arrangements can the students sit?

A.1296
B.1850
C.2880
D.3546
E.4200
Show more

1. If C1 and C2 are the two couples and A, B, C, D are the 4 other persons, these 6 can be arranged in 6! ways
2. Each of the 2 couples can be arranged in 2! ways, so totally, 2!*2! = 4 ways
3. Therefore for each arrangement in (1), there are 4 arrangements as given in (2)
4. Total number of arrangements is 6! *4= 2880 ways
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A group of 8 students take up a full row at a movie theater 05 Sep 2013, 01:18
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Bunuel
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A group of 8 students take up a full row at a movie theater. There are 2 couples and the 2 people within each couple must sit together. in how many arrangements can the students sit?

A.1296
B.1850
C.2880
D.3546
E.4200

Glue couples together: {AB}, {CD}.

6 units {AB}, {CD}, {E}, {F}, {G}, {H} can be arranged in 6! ways. Each couple within their unit can be arranged in 2! ways.

Therefore the final answer is 6!*2!*2!=2,880.

Answer: C.

Bunuel,
Thanks for your explanation but I'm getting confused with this part "There are 2 couples and the 2 people within each couple must sit together" particularly...

As we do 6!, how then can two people within each couple must sit together as per the above statement?

Please help!
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It just means that each couple must sit together.
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A group of 8 students take up a full row at a movie theater 05 Sep 2013, 03:52
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OK! that makes it clear...

Thanks Bunuel :)
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A group of 8 students take up a full row at a movie theater 04 Jun 2025, 12:59
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