6 person are seated at a round table. What is the probability that 2 particular persons sit together?
call the two particular persons, A, B
@perl
@ganeshie8 . Number of ways 6 persons sit on a round table = (6 - 1)! = 5! .-. n(S) = 5! Since two persons always sit together, we con- sider them one. So, total persons are 4 + 1 = 5 .•. Number of ways these 5 persons sits on the round table is (5 - 1)! = 4! ways and these two persons sit in 2! ways among themselves. N(E)=4!*2! N(E)/N(S)=2/5
put A and B in the box `AB`
now total persons :- `AB`P1,P2,P3,P4 total number of persons=5
arrange them in a circle :- (n-1) !=((5-1)!
total outcomes :- (6-1) !
and we can arrange AB in two ways like AB and BA so,multiply by 2 ! so,we get 4 !*2!
\[\large \bf probability=\frac{4! \times 2!}{5!}\]
why we taking AB in one box.that is confusing meand why we are taking circular seating for (n-1)!
i mean the two particular persons be A and B and they want to sit together so i put them in box or simply you can say that they never separate
REMEMBER :- In circular permutation,we arrange `n` people in `(n-1) !` and in linear or simple permutation,we arrange `n`people in `n!`
hope you understand @dg2
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