You are asked to distribute 10 balls into three groups: 2 balls, 3 balls, and 5 balls. (a) if the 10 balls are indistinguishable, how many different arrangements can you have

In how many ways can 20 identical balls be distributed into 4 distinct boxes subject? a) With no constraints. b) Each box gets at least two balls. c) Box 1 gets exactly one ball and box 2 gets at least one ball. d) Each box gets an even number of balls.