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How many solutions in positive integers does $x + y + z = 12$ have?

Competition practicePermutations & Combinations

A91
B66
C45
D55

Step-by-Step Solution

Positive parts: choose 2 of the 11 gaps between 12 units,

^{11} C_{2} = 55. (91 =^{14} C_{2}

counts non-negative solutions.)

Answer: D) 55

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