[Math] If a group consists of five girls and five boys, what is the probability that all girls will end up on the same team

Question

$10$ kids are grouped into an A team with $5$ kids and a B team with five kids.
If the group consists of five girls and five boys, what is the probability that all girls will end up on the same team

Here is my thought process for this problem:
Choosing first person for Team A, there is a $\frac{5}{10}$ chance girl will be chosen, choosing next person for Team B, $\frac49$ chance of being girl, etc. For simplicity I'll call this $R$.

I believe the solution is $2\cdot R$ since there are two possible teams and either could have the all girl composition

is this correct?

Answer 1

Pick any one of the girls.   She will be on one of the two teams but who cares which.   What we are after is the probability that the other four girls, selected from the other nine players, will also be on her team.

$$\dfrac{1}{\binom{9}{4}}$$