MeghaP wrote:
chetan2u wrote:
chetan2u wrote:
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) \(\frac{8}{9}\)
.
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
I did not do this using the formula for circular permutations and took the total no. of ways to be 10! Does this formula hold true in all circular arrangements. I would really appreciate if you could explain as to how we can derive this. Apologies if this is a very basic question but just wanted to make sure i have got the concepts right. Thanks for your help.
Hi,
the formula for circular permutations is (n-1)! as against n! in a row AND it is valid for all circular arrangements AND it also finds its place in ACTUAL GMAT.NOW WHY of it?If you are seating 4 people in a row, you can seat them in 4! ways..
However in circular permutations it becomes (4-1)=3!...
When you shift each person in a ROW by one place, it is a different arrangement
for example a,b,c,d is different from d,a,b,c or c,d,a,b or b,c,d,a..But it is not the case in circular permutations/arrangements..
When you shift them by one seat each, the relative position of each other does NOT change..Draw a circle place a,b,c,d AND then d,a,b,c-- you will find they are the same
this is the reason for (n-1)! as against n! in a row
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
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