2020 · Q4
The number of different solutions of the equation x + y + z = 12, where each of x, y and z is a positive integer, is
Elementary MathematicsNumber System
- A53
- B54
- C55
- D56
Explanation
Put a = x-1, b = y-1, c = z-1 (all >= 0); then a+b+c = 9. By stars-and-bars the number of non-negative solutions is C(9+3-1, 2) = C(11,2) = 55. Hence option (C).