The number of triplets x , y , z where x , y , z are distinct non negative integers satisfying x + y + z = 15 , is

Step-by-step solution

Given, x + y + z = 15 Now we know that, Non-negative integral solution of equation a + b + c = n is given by C 3 - 1 n + 3 - 1 where a = b = c   &   a = b ≠ c are also possibilities So by above formula we get, Total number of non-negative solution will be, C 3 - 1 15 + 3 - 1 = C 2 17 Now solving If any of these 2 are equal So, the equation will become   x + 2 y = 15 Now finding possible cases we get, y = 0 x = 15 y = 1 x = 13 y = 2 x = 11 y = 3 x = 9 y = 4 x = 7 y = 5    x = 5 &#8