The number of non-negative integral solutions of the equation x + y + 3 z = 33 is

Step-by-step solution

x + y = 33 - 3 z Here, z will vary from 0 to 11 The number of required solutions = ∑ z = 0 11 C 33 - 3 z + 2 - 1 2 - 1 = ∑ z = 0 11 C 34 - 3 z 1 = ∑ z = 0 11 34 - 3 z = 34 × 12 − 3 ⋅ 11 × 12 2 = 34 × 12 - 33 × 6 = 210 .