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04 Mar 2021, 03:15
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
29% (02:12) correct
71%
(02:07)
wrong
based on 86
sessions
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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
A. 72
B. 144
C. 288
D. 576
E. 1152
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
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
11 Feb 2022, 12:35
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CrackverbalGMAT
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
