NDA Mathematics Question (2026) — Solution

Step-by-step solution

Total number of outcomes when four dice are rolled is 6^4 = 1296. Let x_1, x_2, x_3, x_4 be the numbers appearing on the four dice. We need to find the number of solutions to the equation: x_1 + x_2 + x_3 + x_4 = 6 where 1 x_i 6 for i = 1, 2, 3, 4. Let x_i = y_i + 1, where y_i 0. Substituting this into the equation, we get: (y_1 + 1) + (y_2 + 1) + (y_3 + 1) + (y_4 + 1) = 6 y_1 + y_2 + y_3 + y_4 = 2 The number of non-negative integer solutions to this equation is given by ^ n+r-1 C_ r-1 , where n=2 and r=4. Number of favorable outcomes = ^ 2+4-1 C_ 4-1 = ^ 5 C_ 3 = 10. The required probability is 10 1296 = 5 648 . Answer: 5 648