Ordering solutions (permutation 2)

Discrete Mathematics Level 4

Find the number of positive integral solutions of \( x + y + z + w = 20\) under the following conditions:

  1. No variable may exceed 10; Zero values excluded.

  2. Zero values are excluded.

  3. Zero values of \(x, y, z, w\) are included

  4. Each variable is an odd number.

  5. \(x, y, z, w\) have different values (zero excluded).

Post your answer as decreasing order of the answers obtained.


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