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A man, his wife, and his four daughters are being seated around a rect

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A man, his wife, and his four daughters are being seated around a rect  [#permalink]

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New post 28 Dec 2016, 01:51
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Question Stats:

73% (01:22) correct 27% (01:34) wrong based on 141 sessions

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A man, his wife, and his four daughters are being seated around a rectangular table. The man and his wife must sit across from each other alone at each end of the table. The daughters are to be seated two on each side. How many different seating arrangements are there at this table?

A. 12
B. 24
C. 48
D. 120
E. 720

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Re: A man, his wife, and his four daughters are being seated around a rect  [#permalink]

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New post 28 Dec 2016, 01:56
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Bunuel wrote:
A man, his wife, and his four daughters are being seated around a rectangular table. The man and his wife must sit across from each other alone at each end of the table. The daughters are to be seated two on each side. How many different seating arrangements are there at this table?

A. 12
B. 24
C. 48
D. 120
E. 720


IMO: C

we have select 2 out four first, which can be done by 4p2

and they can rearrange themselves by 2

and the parent can switch their position also, so X 2

total 48
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A man, his wife, and his four daughters are being seated around a rect  [#permalink]

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New post 28 Dec 2016, 04:07
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Bunuel wrote:
A man, his wife, and his four daughters are being seated around a rectangular table. The man and his wife must sit across from each other alone at each end of the table. The daughters are to be seated two on each side. How many different seating arrangements are there at this table?

A. 12
B. 24
C. 48
D. 120
E. 720


There are 6 seats available. Let's say X1,X2,X3,X4,X5 and X6.
But as per the constraint the man and his wife can be accommodated in only X1 and X4. So they can be accommodated in 2 ways(M-X1, W-X4 or M-X4, W- X1)
Then 4 girls are available with 4 seats. n items can be arranged in n! ways. So the 4 girls can be arranged in 4! ways = 24ways.
So, total number of arrangements possible is 24*2=48 ways.



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Re: A man, his wife, and his four daughters are being seated around a rect  [#permalink]

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New post 08 Sep 2017, 09:56
1
Bunuel wrote:
A man, his wife, and his four daughters are being seated around a rectangular table. The man and his wife must sit across from each other alone at each end of the table. The daughters are to be seated two on each side. How many different seating arrangements are there at this table?

A. 12
B. 24
C. 48
D. 120
E. 720



We have to seat for daugters - it is just as to seat 4 people in a line - 4! ways.
Now, seats of man and his wife are fixed at edgesof the table. Bit still. One of the, can sit at one end or at another. 2! ways.

The answer: 4!*2! = 48.
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Re: A man, his wife, and his four daughters are being seated around a rect   [#permalink] 08 Sep 2017, 09:56
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