# Front-loaded Boxes

**Discrete Mathematics**Level 5

Six boxes labeled \(1,2, \ldots, 6\) are arranged in a line. Seven identical balls are to be placed into the boxes such that for any \(1 \leq k \leq 6,\) there are at least \(k\) total balls amongst boxes \(1,2 , \ldots k.\) How many different placements of the balls into the boxes are possible?

**Details and assumptions**

All 7 balls have to be placed.