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17 Feb 2021, 06:00
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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:
44% (02:38) correct
56%
(02:07)
wrong
based on 85
sessions
History
Date
Time
Result
Not Attempted Yet
Six person A, B, C, D, E and F are to be seated at a circular table. The number of ways this can be done if A must have either B or C on his right and B must have either C or D on his right is:
(A) 36
(B) 30
(C) 24
(D) 18
(E) 12
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
(A) 36
(B) 30
(C) 24
(D) 18
(E) 12
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
18 Feb 2021, 21:56
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There are 3 possible cases
1) when A, B and C are sitting together (in the same order)
Possible combinations= (4-1)!=6
2)when A, B and D are sitting together (in the same order)
Possible combinations= (4-1)!=6
3) when A and C are sitting together and B and D are sitting together
Possible combinations= (4-1)!=6
The number of ways this can be done if A must have either B or C on his right and B must have either C or D on his right is:6+6+6=18
1) when A, B and C are sitting together (in the same order)
Possible combinations= (4-1)!=6
2)when A, B and D are sitting together (in the same order)
Possible combinations= (4-1)!=6
3) when A and C are sitting together and B and D are sitting together
Possible combinations= (4-1)!=6
The number of ways this can be done if A must have either B or C on his right and B must have either C or D on his right is:6+6+6=18
Bunuel
07 Mar 2021, 13:02
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Bunuel
Solution:
If B is on the right of A, then either A, B and C will sit together in that order, or A, B and D sit together in that order. In the former case, we can think of [ABC] as a single unit and calculate the number of ways of seating [ABC], D, E and F around a circular table. This can be done in (4 - 1)! = 3! = 6 ways. In the latter case, we can apply a similar argument and conclude that there are also 6 ways.
If C is on the right of A, then D must be on the right of B. Thus, we are actually seating [AC], [BD], E and F around the circular table. Again since there are four items, there are (4 - 1)! = 3! = 6 ways of seating the six people this way.
In total, there are 6 + 6 + 6 = 18 ways.
Answer: D
