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In how many ways can 10 be written as an ordered sum of positive whole numbers (for example 3+7 and 7+3 count separately, and 10 itself counts)?

Competition practicePermutations & Combinations
  • A1024
  • B42
  • C512
  • D256

Step-by-Step Solution

Write ten 1's in a row; there are 9 gaps. Each gap either gets a '+' break or not: . (42 counts unordered sums, i.e. partitions.)
Answer: C) 512

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