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Adam, Bob, Carol, Diane, and Ed are all sitting on a bench. If Adam an

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Adam, Bob, Carol, Diane, and Ed are all sitting on a bench. If Adam an  [#permalink]

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New post 03 Apr 2017, 00:34
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A
B
C
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E

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Adam, Bob, Carol, Diane, and Ed are all sitting on a bench. If Adam and Diane must sit next to each other, how many different seating arrangements are possible on the bench?

A. 4
B. 8
C. 10
D. 48
E. 120

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Re: Adam, Bob, Carol, Diane, and Ed are all sitting on a bench. If Adam an  [#permalink]

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New post 03 Apr 2017, 02:25
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Bunuel wrote:
Adam, Bob, Carol, Diane, and Ed are all sitting on a bench. If Adam and Diane must sit next to each other, how many different seating arrangements are possible on the bench?

A. 4
B. 8
C. 10
D. 48
E. 120


Since Adam and Diane must sit next to each other, lets consider them as a single entity X.
Therefore we have Bob, Carol, Ed and X

different seating arrangements = 4! * 2! = 24*2 = 48

4! ==> ways to arrange Bob, Carol, Ed and X on a bench
2! ==> since Adam and Diane can switch the seats between themselves

Hence option D is correct
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Re: Adam, Bob, Carol, Diane, and Ed are all sitting on a bench. If Adam an  [#permalink]

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New post 03 Apr 2017, 07:54
Bunuel wrote:
Adam, Bob, Carol, Diane, and Ed are all sitting on a bench. If Adam and Diane must sit next to each other, how many different seating arrangements are possible on the bench?

A. 4
B. 8
C. 10
D. 48
E. 120


Since A & D must be together, we can consider total 4 entities (B,C, E & "AD")
thus ways to arrange these 4 = 4! = 24
and internally "AD" can be arranged in 2 ways
Hence, total ways = 24 x 2 = 48
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Re: Adam, Bob, Carol, Diane, and Ed are all sitting on a bench. If Adam an  [#permalink]

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New post 06 Apr 2017, 09:34
Bunuel wrote:
Adam, Bob, Carol, Diane, and Ed are all sitting on a bench. If Adam and Diane must sit next to each other, how many different seating arrangements are possible on the bench?

A. 4
B. 8
C. 10
D. 48
E. 120


Let’s denote Adam, Bob, Carol, Diane, and Ed as A, B, C, D, and E, respectively.

If Adam and Diane must sit together, we can consider them as one person [AD]. For example, one seating arrangement could be [AD][B][C][E]. Thus, the number of ways to arrange four people in a row is 4! = 24.

However, we must also account for the ways we can arrange Adam and Diane, which could be either [AD] or [DA], which is 2! = 2 ways.

Therefore, the total number of seating arrangements is 24 x 2 = 48.

Answer: D
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Re: Adam, Bob, Carol, Diane, and Ed are all sitting on a bench. If Adam an &nbs [#permalink] 06 Apr 2017, 09:34
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