What is the number of positive integer solutions of x + y + z = 5 ?

Step-by-step solution

The number of positive integer solutions to the equation x₁ + x₂ + + x_r = n is given by ^ n-1 C_ r-1 . For the given equation x + y + z = 5 , we have n = 5 and r = 3 . The number of positive integer solutions is ⁵⁻¹C_ 3-1 = ⁴C₂ . ⁴C₂ = 4 3 2 1 = 6 . Answer: 6