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Gita, Hussain, Inge, Jeong, Karen, and Leila are seated in a row of

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Gita, Hussain, Inge, Jeong, Karen, and Leila are seated in a row of  [#permalink]

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New post 25 Aug 2014, 12:41
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Difficulty:

  75% (hard)

Question Stats:

54% (02:16) correct 46% (02:25) wrong based on 133 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
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Re: Gita, Hussain, Inge, Jeong, Karen, and Leila are seated in a row of  [#permalink]

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New post 25 Aug 2014, 23:26
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usre123 wrote:
I understand how we first band together J and L, and get 5! = 120. Then because J and L can switch places, we have 5! * 2= 240.



This is correct. There are 240 ways in which you can make the 6 people sit together such that J and L are together. Now, forget it.

Think about the number of ways in which you can make I and G sit together while J and L are sitting together:

J and L are tied together and now we tie I and G together. So we have 4 individuals/pairs. We can arrange them in 4! ways but J and L can switch places and so can I and G. So total number of ways = 4! * 2 * 2 = 96

There are 96 ways in which I and G will be together and J and L will also be together.

So in 240 - 96 = 144 ways I and G will not be together while J and L will be together.
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Re: Gita, Hussain, Inge, Jeong, Karen, and Leila are seated in a row of  [#permalink]

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New post 25 Aug 2014, 12:46
1
I understand how we first band together J and L, and get 5! = 120. Then because J and L can switch places, we have 5! * 2= 240.

Now for I and G not sitting together, let's calculate for when they do sit together ( and assuming J and L are already sitting together):
4! =24
So now I and G can switch, so 24 x 2= 48.
So my final answer is 240- 48 =196.
I don't understand why we must accommodate for J and L switching, as I've already done that in the first part.

Thanks.
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Re: Gita, Hussain, Inge, Jeong, Karen, and Leila are seated in a row of  [#permalink]

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New post 25 Aug 2014, 13:15
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I am taking he initials of each for refernce... Since, J and L have to be together, lets combine them into 1. So, now we have 5 things which can be arranged in 5! ways. ALso, J and L can be arranged in two ways (JL, LJ) .
This gives total ways, 5! * 2 = 240

Now, we are given G and I can not be together, therefore subtract the cases when they (G and I) are together. Now, see we have 4 people (JL and GI) are comined as one. Total no of arrangement = 4!
But, J and L can be arranged internally in 2 ways (JL and LJ). Similarly, G and I can be internally arranged in two ways (GI and IG).
Therefore, total such cases will be 4! * 2 * 2 = 96. Subtract this from 240.
240 - 96 = 144. Hence, C
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Re: Gita, Hussain, Inge, Jeong, Karen, and Leila are seated in a row of  [#permalink]

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New post 02 Aug 2018, 11:54
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