A Weighty Problem Puzzle

[Masuma Parvin]

A Weighty Problem
I have ten boxes which I want to pack into crates. Each crate can carry a maximum of 25 kg.

But I only have three crates, and the total weight of the boxes is 75kg:

15 kg, 13kg, 11 kg, 10 kg, 9 kg, 8 kg, 4 kg, 2 kg, 2kg, 1 kg

How can I pack the boxes into the crates?
The solution is:
Our Solution:
Ten possible answers :

{Crate 1}, {Crate 2}, {Crate 3}
{15,10}, {13,8,4}, {11,9,2,2,1}
{15,10}, {13,11,1}, {9,8,4,2,2}
{15,10}, {11,8,4,2}, {13,9,2,1}
{15,10}, {11,9,4,1}, {13,8,2,2}
{11,10,4}, {15,8,2}, {13,9,2,1}
{11,10,4}, {15,9,1}, {13,8,2,2}
{13,8,4}, {15,9,1}, {11,10,2,2}
{13,10,2}, {15,8,2}, {11,9,4,1}
{13,10,2}, {15,9,1}, {11,8,4,2}
{13,11,1}, {15,8,2}, {10,9,4,2}

[msu_math]

This inspection shows that there are 10 ways to pack the boxes into the crates. Is there any mathematical argument to prove that "no other ways are left to pack the boxes" ?