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15 Feb 2021, 09:30
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B
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Difficulty:
65%
(hard)
Question Stats:
63% (02:29) correct
37%
(02:28)
wrong
based on 166
sessions
History
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Time
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Not Attempted Yet
Six people are going to sit in a row on a bench. A and B are adjacent, C does not want to sit adjacent to D. E and F can sit anywhere. Number of ways in which these six people can be seated, is
(A) 200
(B) 144
(C) 120
(D) 56
(E) 46
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
(A) 200
(B) 144
(C) 120
(D) 56
(E) 46
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
15 Feb 2021, 09:47
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Bunuel
Let us take A and B together as one person.
So total ways to sit (AB),C,D,E,F will be 5!*2, where 2 comes as A and B can be arranged in two ways.
Let us now take ways in which C and D are together.
So AB is taken as one and CD as one then ways =4!*2*2
Final ways = 5!*2-4!*2*2=120*2-24*4=240-96=144
B
09 Mar 2021, 14:18
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Bunuel
Solution:
If the restriction is only on A and B and not on C and D, then we can have, for example, [AB]-C-D-E-F. That is, AB is a group and can be considered as “one” person, so the number of sitting arrangements is 5! = 120. However, since within the group of [AB], it can be either AB or BA, we have to multiply 120 by 2 and obtain 240.
Now, let’s see of these 240 arrangements, how many have C and D also sitting next to each other. That is, we can have, for example, [AB]-[CD]-E-F. That is, both AB and CD can each be considered as “one” person, so the number of sitting arrangements is 4! = 24. However, since within the group of [AB], it can be either AB or BA and within the group of [CD], it can be either CD or DC, we have to multiply 24 by 2 by 2 and obtain 96.
However, since the problem actually says the opposite has to happen, i.e., that C and D can’t sit next to each other, we have to subtract 96 from 240 and obtain 144 as the final answer.
Answer: B
