programming - Best way to find permutation with specific total

Can anyone suggest a good way to find permutations of 12 digits, 0 to 4, totalling 24.

I.e. two such permutations:-

{2, 1, 4, 1, 2, 2, 2, 2, 2, 2, 1, 3} // Total

24

{4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0} // Total

24

I am trying this, but it takes too long:-

FromDigits[{4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0}, 5]

244125000

list = {};
Array[If[Total[IntegerDigits[#, 5]] == 24, list = {list, #}] &, 244125000];

Answer

Use the following

IntegerPartitions[24, {12}, {0, 1, 2, 3, 4}]


(* Out = {{4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0}, {4, 4, 4, 4, 4, 3, 1, 0, 0, 0, 
  0, 0}, {4, 4, 4, 4, 4, 2, 2, 0, 0, 0, 0, 0}, {4, 4, 4, 4, 4, 2, 1, 
  1, 0, 0, 0, 0}, {4, 4, 4, 4, 4, 1, 1, 1, 1, 0, 0, 0}, {4, 4, 4, 4, 
  3, 3, 2, 0, 0, 0, 0, 0}, {4, 4, 4, 4, 3, 3, 1, 1, 0, 0, 0, 0}, {4, 
  4, 4, 4, 3, 2, 2, 1, 0, 0, 0, 0}, {4, 4, 4, 4, 3, 2, 1, 1, 1, 0, 0, 
  0}, {4, 4, 4, 4, 3, 1, 1, 1, 1, 1, 0, 0}, {4, 4, 4, 4, 2, 2, 2, 2, 
  0, 0, 0, 0}, {4, 4, 4, 4, 2, 2, 2, 1, 1, 0, 0, 0}, {4, 4, 4, 4, 2, 
  2, 1, 1, 1, 1, 0, 0}, {4, 4, 4, 4, 2, 1, 1, 1, 1, 1, 1, 0}, {4, 4, 
  4, 4, 1, 1, 1, 1, 1, 1, 1, 1}.... *)

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