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3 married couples have to be arranged on 6 seats in a row, such that n
[#permalink]
25 Aug 2026, 01:52
25 Aug 2026, 01:52
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Question Stats:
50% (03:34) correct
50% (01:56) wrong based on 6 sessions
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3 married couples have to be arranged on 6 seats in a row, such that none of the couples is separated. If the husband from Couple 1 and the husband from Couple 2 must not sit next to each other, in how many ways can the 6 people be arranged?
(A) 16
(B) 32
(C) 40
(D) 44
(E) 48
(A) 16
(B) 32
(C) 40
(D) 44
(E) 48
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Re: 3 married couples have to be arranged on 6 seats in a row, such that n
[#permalink]
25 Aug 2026, 16:46
25 Aug 2026, 16:46
Let the 3 couples be AaBbCc
Let husband of couple 1 be a and husband of couple 2 be b
Number of ways the 3 couples can sit without separation and without any other restriction
3! 2! 2! 2! = 48
Number of ways a and b can sit together
AabBcC........1 x 1 x 2 = 2 ways
BbaACc........1 x 1 x 2= 2 ways
CcAabB........2 x 1 x1 = 2 ways
CcBbaA........2 x 1 x 1 = 2 ways
Total ways = 8
Number of ways they cant sit together 48 - 8 = 40
Let husband of couple 1 be a and husband of couple 2 be b
Number of ways the 3 couples can sit without separation and without any other restriction
3! 2! 2! 2! = 48
Number of ways a and b can sit together
AabBcC........1 x 1 x 2 = 2 ways
BbaACc........1 x 1 x 2= 2 ways
CcAabB........2 x 1 x1 = 2 ways
CcBbaA........2 x 1 x 1 = 2 ways
Total ways = 8
Number of ways they cant sit together 48 - 8 = 40
gmatclubot
Re: 3 married couples have to be arranged on 6 seats in a row, such that n [#permalink]
25 Aug 2026, 16:46
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