i have the following problem.
There are 7 different kind of balls and 10 boxes. The balls are distributed into the boxes so that each box must contain 5 different balls.
Prove that at least one type of ball appears in at least 8 boxes.
I have a proof to this but i dont understand it.
proof with contradiction:
Distribute 10*5 = 50 balls
Assumption: There is no kind of ball in more than 7 boxes.
How many balls can you at the most distribute, under the assumption? -> 7*7 = 49,
there are not enough balls (this is the contradiction).
I dont understand how this makes sense. Why is this the contradiction?