Ordering solutions (permutation 2)

Find the number of positive integral solutions of x + y + z + w = 20 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 x, y, z, w are included

  4. Each variable is an odd number.

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

Post your answer as decreasing order of the answers obtained.


The answer is 32154.

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1 solution

Prince Loomba
May 8, 2016

3. 3. ( 23 3 ) 23\choose 3 2. 2. ( 19 3 ) 19\choose 3 1. 1. ( 19 3 ) 19\choose 3 4 × -4\times ( 9 3 ) 9\choose 3 5. 552 5.\quad552 4. \quad4. ( 11 8 ) 11\choose 8

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