We are given 8 chiildren: 4 boys and 4 girls. We are dividing them into 2 groups (A and B) - 4 people each. What is the propability that 4 boys (and so 4 girls) will be in the same group?

B = Boys, G = Girls

Well, there are only 5 ways you can group them together:

{B, B, B, B} | {B, B, B, G} | {B, B, G, G} | {B, G, G, G} | {G, G, G, G} (total: 5)

Probability that the two groups will end up in 4 boys and 4 girls is: 2 / 5