A group of $2N$ boys and $2N$ girls is randomly divided into two equal groups. What is the probability that each group has the same number of boys and girls?
I had a few ideas on this question. Since both groups must have the same number of boys and girls, i counted the numer of ways to form up pairs of boys and girls. Then, i counted the number of ways to divided those pairs into two groups, and since this number of pairs is even, those new groups would be equal in number. Dividing by the number of ways to form up two distinct groups with everybody, this would give me the probability.
Is this right?