Having a bag of balls of $3$ colors:
- $m$ balls are red
- $n$ balls are blue
- $o$ balls are grey
If $N$ people pick $3$ balls out of the bag, what is the probability that at least one of them will have $3$ either red or blue balls.
The probability of one person doing this should be: $\frac{\binom{m}{3} + \binom{n}{3}}{\binom{m+n+o}{3}}$
I cannot figure out the case with multiple people, because those are not independent events.