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31 Mar 2016, 05:01
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
56% (01:38) correct
44%
(01:37)
wrong
based on 215
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There are 10 students named alphabetically from A to J. What is the Probability that A and D do not sit together if all 10 sit around a circular table?
A) \(\frac{2}{9}\)
B) \(\frac{2}{5}\)
C) \(\frac{7}{9}\)
D) \(\frac{4}{5}\)
E) \(\frac{8}{9}\)
A) \(\frac{2}{9}\)
B) \(\frac{2}{5}\)
C) \(\frac{7}{9}\)
D) \(\frac{4}{5}\)
E) \(\frac{8}{9}\)
31 Mar 2016, 21:48
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chetan2u
There are 10 students named alphabetically from A to J. What is the Probability that A and D do not sit together if all 10 sit around a circular table?
A) \(\frac{2}{9}\)
B) \(\frac{2}{5}\)
C) \(\frac{7}{9}\)
D) \(\frac{4}{5}\)
E) \(\frac{8}{9}\)
.
A) \(\frac{2}{9}\)
B) \(\frac{2}{5}\)
C) \(\frac{7}{9}\)
D) \(\frac{4}{5}\)
E) \(\frac{8}{9}\)
.
Hi,
Since it is circular Permutation, ways= (n-1)!
so the 10 students can be seated in 10-1=9!..
We have to find ways A and D do not seat together..
It is easier to find ways both will seat together..
let A and D be one person. so total person =9..
these 9 can be seated in 9-1=8!
BUT A and D can be seated in 2! within themselves..
so TOTAL ways = 2*8!..
So PROBABILITY that A and D sit together = \(2*\frac{8!}{9!}= \frac{2}{9}\)
Therefore Prob that both do not sit together = \(1-\frac{2}{9}=\frac{7}{9}\)
C
General Discussion
31 Mar 2016, 11:09
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Editing my solution:
Number of students = 10
Number of ways 10 students can sit around a circular table = (10 - 1)! = 9!
Number of ways A and D sit together (consider A and D as one entity) = (9 - 1)! = 8! * 2
Number of ways A and D do not sit together = 9! - (8! * 2)
Probability = (9! - (8! * 2))/9! = 1 - 2/9 = 7/9
Answer: C
Number of students = 10
Number of ways 10 students can sit around a circular table = (10 - 1)! = 9!
Number of ways A and D sit together (consider A and D as one entity) = (9 - 1)! = 8! * 2
Number of ways A and D do not sit together = 9! - (8! * 2)
Probability = (9! - (8! * 2))/9! = 1 - 2/9 = 7/9
Answer: C
