20 girls, among whom are A and B sit down at a round table. The probability that there are 4 girls between A and B is

There are 20 girls in total, out of which two are A and B.

So, out of remaining 18 girls, we need to choose 4 girls so that they can sit between A and B.

Number of ways of choosing these 4 girls = $$^{18}C_4$$

Number of ways of arranging these 4 girls = $$4!$$

Number of ways of arranging the remaining 14 girls = $$14!$$

Also, number of ways in which $$A$$ and $$B$$ can arrange = $$2!$$

So, total number of cases such that there are 4 girls between A and B = $$^{18}C_4\times\ 4!\times\ 14!\times\ 2!$$

Also, number of ways of arranging 20 girls in round table = $$\left(20-1\right)!=19!$$

So, required probability = $$\dfrac{^{18}C_4\times\ 14!\times\ 4!\times\ 2!}{19!}=2\times\ \dfrac{18!}{19!}=\dfrac{2}{19}$$