1. In how many ways can we place r red balls and w white balls in n boxes so that each box conta ins one ball of each color? 2. (a) How many sequences (lists) of m Os and n 1s are there b) How many sequences are there in which each 1 is separated by at least two 0s? (Assume that for this part m 2 2(n - 1).) 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 (c) Constraint B is satisfied (d) Constraints A and B are satisfied