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A dinner party consisting of 5 couples, sit around a rectangular table

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Bunuel
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A dinner party consisting of 5 couples, sit around a rectangular table [#permalink] New post   04 Mar 2021, 03:15
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A dinner party consisting of 5 couples, sit around a rectangular table, with ladies and gentlemen altering. The host and hostess each occupy one end of the table and their guests are arranged four on each side. What is the number of ways the party can be seated? (2 seating arrangements are considered different only when the positions of the people are different relative to each other.)

A. 72
B. 144
C. 288
D. 576
E. 1152
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CrackverbalGMAT
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Re: A dinner party consisting of 5 couples, sit around a rectangular table [#permalink] New post   04 Mar 2021, 04:13
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Let us seat the host and Hostess at 1 end of the table. They can rearrange themselves in 2 ways.

There are 4 seats in which the men can seat alternatively. This can be filled in 4! = 24 ways.

The women will sit in the remaining 4 ways in 4! = 24 ways


Total Arrangements = 2 * 24 * 24 = 1152


Option E

Arun Kumar
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Re: A dinner party consisting of 5 couples, sit around a rectangular table [#permalink] New post   11 Feb 2022, 12:35
CrackverbalGMAT wrote:
Let us seat the host and Hostess at 1 end of the table. They can rearrange themselves in 2 ways.

There are 4 seats in which the men can seat alternatively. This can be filled in 4! = 24 ways.

The women will sit in the remaining 4 ways in 4! = 24 ways


Total Arrangements = 2 * 24 * 24 = 1152


Option E

Arun Kumar





Actually it is mentioned in the question that the position of X is considered to be changed only if the person's position beside X is changed.
In this way, whereever host or hostess sits, if the person beside him/her doesn't change, the position would be considered to be unchanged.

Thus it should be only 24*24 considering the sides of host and hostess fixed ( i.e 4! seats of males and remaining 4! seats on females, 4!*4!).


= 24*24
= 576
Answer D
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varshas044
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Re: A dinner party consisting of 5 couples, sit around a rectangular table [#permalink] New post   11 Oct 2022, 12:34
Bunuel wrote:
A dinner party consisting of 5 couples, sit around a rectangular table, with ladies and gentlemen altering. The host and hostess each occupy one end of the table and their guests are arranged four on each side. What is the number of ways the party can be seated? (2 seating arrangements are considered different only when the positions of the people are different relative to each other.)

A. 72
B. 144
C. 288
D. 576
E. 1152



Let’s see

We have total 10 people (5 couples) --- 5 males and 5 females

1) Head of the table will be 1 male and 1 female; they can only be arranged in one way since their position relative to each other will not change = 1 way
2) On either side of the rectangle (along the length) lets say that we have 2 males and 2 females on each side
We have 4 males and 4 females left
One side: Choices for arranging males = 4 x 3 ------ choices for arranging females = 4 x 3
Other side: choices for arranging males = 2 x1 ---- choices for arranging females = 2x1

total ways = 1x4x3x4x3x2x1x2x1 = 576

Answer – D
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Re: A dinner party consisting of 5 couples, sit around a rectangular table [#permalink]
11 Oct 2022, 12:34
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