A box contains 5 blue, 6 yellow and 4 red balls. The number of ways, of drawing 8 balls containing at least two balls of each colour, is :

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: ⁵C₂ ⁶C₂ ⁴C₄ = 10 15 1 = 150 Case 2: ⁵C₂ ⁶C₃ ⁴C₃ = 10 20 4 = 800 Case 3: ⁵C₂ ⁶C₄ ⁴C₂ = 10 15 6 = 900 Case 4: ⁵C₃ ⁶C₂ ⁴C₃ = 10 15 4 = 600 Case 5: ⁵C₃ ⁶C₃ ⁴C₂ = 10 20