Question: 3. We are given a red box, a blue box and a green box. We are also given 10 red balls, 10 blue balls, and

3. We are given a red box, a blue box and a green box. We are also given 10 red balls, 10 blue balls, and 10 green balls. Balls of the same colour are indistinguishable. Consider the following constraints: A: No box contains a ball that has the same colour as the box. B: No box is empty. Determine the number of ways in which we can put 30 balls into boxes so that:

(a) No constraint has to be satisfied. Every combination is allowed.

(b) Constraint A is satisfied.

(d) Constraints A and B are satisfied.

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