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?

Dear Vivek,

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)

Regards.

i think the answer is 19