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Leaving aside permutations, there are five distict ways of writing the number 4 as the sum of 5 non-negative integers.

  1. 0 + 0 + 0 + 0 + 4
  2. 0 + 0 + 0 + 1 + 3
  3. 0 + 0 + 0 + 2 + 2
  4. 0 + 0 + 1 + 1 + 2
  5. 0 + 1 + 1 + 1 + 1
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Q: In how many ways can you write the number 4 as the sum of 5 nonnegative integars?
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