Given 10 distinguishable balls and 5 distinguishable boxes (such that the boxes can be numbered 1 through 5):

1. How many ways are there to distribute the balls so that all the balls are strictly in the boxes in the set {1,2,3}?
2. Likewise, how many ways can the balls be distributed to boxes 1 through 3 such that **no single box in this set** remains empty.

What is very confusing here is that there are 5 distinguishable boxes in total, and the question strictly asks about three. Given 10 balls, I have no clue how to approach this.