The number of non-negative integral solutions of the equation x + y + z + 5 t = 15 is

Step-by-step solution

x + y + z + 5 t = 15 ,   t ∈ 0 ,1 , 2 ,3 ⇒ x + y + z = 15 - 5 t Number of non-negative integral solutions of x + y + z = 15 - 5 t is equal to 17 - 5 t C 2 = 17 - 5 t 16 - 5 t 2 Hence, the desired number is equal to ∑ t = 0 3 17 - 5 t 16 - 5 t 2 = 17 × 16 2 + 12 × 11 2 + 7 × 6 2 + 2 × 1 2 = 136 + 66 + 21 + 1 = 224