Three randomly chosen non negative integers x , y , z are found to satisfy the equation x + y + z = 10 . Then the probability that z is even, is

Step-by-step solution

Let z = 2 k ,   where k = 0 ,   1 ,   2 ,   3 ,   4 ,   5 ∴         x + y = 10 - 2 k Number of non negative integral solutions ∑ k = 0 5   11 - 2 k C 1 =   ∑ 11 - 2 k = 3 6 Total cases =   10 + 3 - 1 C 3 - 1 = 66 Required probability = 36 66 =   6 11