JEE Main Mathematics Question (2026) — Solution

Step-by-step solution

Let B, Y, and R be the number of blue, yellow, and red balls drawn respectively. We are given B + Y + R = 8 with B 2, Y 2, and R 2. The possible combinations for (B, Y, R) are: Case 1: (2, 2, 4) Case 2: (2, 3, 3) Case 3: (2, 4, 2) Case 4: (3, 2, 3) Case 5: (3, 3, 2) Case 6: (4, 2, 2) The number of ways for each case is calculated as follows: Case 1: ^ 5 C_ 2 ^ 6 C_ 2 ^ 4 C_ 4 = 10 15 1 = 150 Case 2: ^ 5 C_ 2 ^ 6 C_ 3 ^ 4 C_ 3 = 10 20 4 = 800 Case 3: ^ 5 C_ 2 ^ 6 C_ 4 ^ 4 C_ 2 = 10 15 6 = 900 Case 4: ^ 5 C_ 3 ^ 6 C_ 2 ^ 4 C_ 3 = 10 15 4 = 600 Case 5: ^ 5 C_ 3 ^ 6 C_ 3 ^ 4 C_ 2 = 10 20 6 = 1200 Case 6: ^ 5 C_ 4 ^ 6 C_ 2 ^ 4 C_ 2 = 5 15 6 = 450 Total number of ways = 150 + 800 + 900 + 600 + 1200 + 450 = 4100 Answer: 4100