Sure. Limit families to four children. There's one way to have zero daughters. In BBBB, each of the four boys has 3 brothers. Score 12 for the boys here. Th

Sure. Limit families to four children. There's one way to have zero daughters. In BBBB, each of the four boys has 3 brothers. Score 12 for the boys here. There's four ways to have one daughter. In each of them, she's got 3 brothers, while the 3 boys each have 2 brothers. Score 12 for the girls, 24 for the boys. There's six ways to have two daughters. In each of them, the 2 girls each have 2 brothers, while the 2 boys each have 1 brother. Score 24 for the girls, 12 for the boys. There's four ways to have three daughters. In each of them, the 3 girls each have one brother, and the boy has none. Score 12 for the girls, zero for the boys. There's one way to have four daughters, but obviously nobody has a brother. Add up the scores, and you'll see a tie at 48. (EDIT: Bogus expected value removed after re-reading.)