There are a total of 9 red discs and 7 black disks. The bags have been mixed thoroughly, so it is almost as if the contents have been dumped onto the ground and mixed. After mixing, there are 9 discs in the first bag. The probability of there being exactly three is:

The first three terms account for there being 3 red discs, and the last six terms account for there being 6 black discs.