Three girls and four boys are seated randomly on a straight bench. Find the probability that the girls sit together and the boys sit together.

There is a total of 7! possible ways in which the seven children can be seated on the bench. The number of favourable arrangements when four boys are seated on one side and three girls on the other side is 4! * 3! as the boys can be sitting in any order, and so can the girls. We need to multiply this number by 2, because the boys and girls could be seated on either side of the bench, giving us twice as many possibilites. The probability is calculated as the ratio between the number of favourable arrangements and the total number of arrangements, giving us P = (4! * 3! * 2)/(7!) = (3! * 2)/(567) = (322)/(235*7) = 2/35.