I am reading probability notes from : http://www.stat.berkeley.edu/~aldous/134/gravner.pdf On page $8$, there is this question : We have a bag that contains $100$ balls, $50$ of them red and $50$ blue. Select $5$ balls at random. What is the probability that $3$ are blue and $2$ are red?
The answer suggested is $\dfrac{\dbinom{50}{3} \times \dbinom{50}2}{\dbinom{100}5}$.
Here $\dbinom{50}{3}$ means ways to choose $3$ out of $50$.
Does not this answer assumes all red/blue balls are distinct form other red/blue balls, though never mentions in problem.
I think it is not correct.
What I think :
Total number of ways ball can be selected is $2^5$. Ball can be either red or blue. Total favorable events : $\dbinom{5}3$ or $\dbinom{5}2$ i.e. places where red or blue balls can be placed. And thus probability is $\dfrac{\dbinom{5}3}{2^5}$
I understand notes can have some bug. Help me to understand which method is correct.