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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
Gita, Hussain, Inge, Jeong, Karen, and Leila are seated in a row of
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16 Jul 2021, 22:31
16 Jul 2021, 22:31
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Question Stats:
62% (02:24) correct
37% (02:32) wrong based on 24 sessions
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Gita, Hussain, Inge, Jeong, Karen, and Leila are seated in a row of six chairs. How many seating arrangements are possible if Gita cannot sit next to Inge and Jeong must sit next to Leila?
(A) 288
(B) 240
(C) 144
(D) 120
(E) 96
(A) 288
(B) 240
(C) 144
(D) 120
(E) 96
Gita, Hussain, Inge, Jeong, Karen, and Leila are seated in a row of
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17 Jul 2021, 09:03
17 Jul 2021, 09:03
2
Here we have G,H, I, J, K and L.
Lets take JL as one item, and G,H,I and K as other items. So, now we have 5 items to arrange = 5! = 120
But we CANNOT let G and I sit together. Lets find out in how ways among above arrangements G and I do sit together.
Take JL and GI as two items, and H and K as other items. In total, we have got 4 items to arrange = 4! = 24
Therefore, excluding those in which G and I sit together, we will have 120 - 24 = 96 ways to seat them all.
The correct answer is E.
Lets take JL as one item, and G,H,I and K as other items. So, now we have 5 items to arrange = 5! = 120
But we CANNOT let G and I sit together. Lets find out in how ways among above arrangements G and I do sit together.
Take JL and GI as two items, and H and K as other items. In total, we have got 4 items to arrange = 4! = 24
Therefore, excluding those in which G and I sit together, we will have 120 - 24 = 96 ways to seat them all.
The correct answer is E.
Re: Gita, Hussain, Inge, Jeong, Karen, and Leila are seated in a row of
[#permalink]
20 Jul 2021, 18:54
20 Jul 2021, 18:54
2
I got this wrong the first time. Where did I go wrong? Well here it is.
We have G,H, I, J, K and L.
Lets take JL as one item, and G,H,I and K as other items. So, now we have 5 items to arrange = 5! = 120 ( Not included arrangements in which LJ sit together; JL is different arrangement from LJ)
Correction: 5! * 2 = 120 * 2 = 240
But we CANNOT let G and I sit together. Lets find out in how ways among above arrangements G and I do sit together.
Take JL and GI as two items, and H and K as other items. In total, we have got 4 items to arrange = 4! = 24 (Again, I did not include JL and IG)
Correction: 2 * 2 * 4! = 24 * 4 = 96
Therefore, excluding those in which G and I sit together, we will have 120 - 24 = 96 ways to seat them all.
Correction: 240 - 96 = 144
We have G,H, I, J, K and L.
Lets take JL as one item, and G,H,I and K as other items. So, now we have 5 items to arrange = 5! = 120 ( Not included arrangements in which LJ sit together; JL is different arrangement from LJ)
Correction: 5! * 2 = 120 * 2 = 240
But we CANNOT let G and I sit together. Lets find out in how ways among above arrangements G and I do sit together.
Take JL and GI as two items, and H and K as other items. In total, we have got 4 items to arrange = 4! = 24 (Again, I did not include JL and IG)
Correction: 2 * 2 * 4! = 24 * 4 = 96
Therefore, excluding those in which G and I sit together, we will have 120 - 24 = 96 ways to seat them all.
Correction: 240 - 96 = 144
