Four persons are chosen at random from a group of 3 men, 2 women and 4 children. The chance that exactly 2 of them are children is:

Choosing 2 of the 4 children can be done in 6 ways and 2 of the other 5 people in 10 ways, so 60 favourable choices. All choices of 4 from 9 number 126, giving 60 / 126 = 10/21. The answer 2/9 forgets to count the ways of picking the two non-children.