6 male students and 3 female students sit around a round table. The probability that no 2 female students sit beside each other can be expressed as a/b, where a and b are coprime positive integers. What is the value of a+b?

Solution) For no female to sit beside each other the females should sit in alternate places.
let the males also occupy alternate places then the no. of arrangements for male= (6-1)!=5!  (circular permut.)
the females can be give the 6 vacant places but there are only 3 female so arrangements= 6-P-3=20
hence total no. of favourable outcomes= 20 . 5!
and total outcomes= (9-1)!=8!
hence P(e)= 20.5!/8!=20/8.7.6=5/84
HENCE a+b=5+84=89(ANS)