What is the number of positive integer solutions of x+y+z=5?
- A. 3
- B. 5
- C. 6 ✓
- D. 9
Correct Answer: C. 6
Explanation
The number of positive integer solutions to x_1 + x_2 + \dots + x_r = n is \binom{n-1}{r-1}. Here n=5 and r=3, so the number of solutions is \binom{5-1}{3-1} = \binom{4}{2} = 6.
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