algorithm for randomly distributing objects with constraints

Help me find a good algorithm?

I have a bag full of n balls. (Let's say 28 balls for an example.)

The balls in this bag each have 1 color. There are <= 4 different colors of balls in the bag. (Let's say red, green, blue, and purple are possibilities.)

I have three buckets, each with a number of how many balls they need to end up with. These numbers total n. (For example, let's say bucket A needs to end up with 7 balls, bucket B needs to end up with 11 balls, bucket C needs to end up with 10 balls.)

The buckets also may or may not have color restrictions - colors that they will not accept. (Bucket A doesn't accept purple balls or green balls. Bucket B doesn't accept red balls. Bucket C doesn't accept purple balls or blue balls.)

I need need to distribute the balls efficiently and randomly (equal probability of all possibilities).

I can't just randomly put balls in buckets that have space and accept them, because that could bring me to a situation where the only bucket that has space left in it does not accept the only color that is left in the bag.

It is given that there is always at least 1 possibility for distributing the balls. (I will not have a bag of only red balls and some bucket with number > 0 doesn't accept red balls.)

All of the balls are considered distinct, even if they are the same color. (The probability of bucket C getting red ball 1 needs to be the same as and independent from the probability of bucket C getting red ball 2.)