NDA Mathematics Question (2025) — Solution

Step-by-step solution

The number of positive integer solutions to the equation x_1 + x_2 + + 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 ^ 5-1 C_ 3-1 = ^ 4 C_ 2 . ^ 4 C_ 2 = 4 3 2 1 = 6. Answer: 6